লগ ইননিবন্ধন
বিষয়সমূহ

PrepBank · বিষয়ভিত্তিক প্রশ্ন

Time & Work, Chain Rule

মোট প্রশ্ন১,০৭৬এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Time & Work, Chain Rule

PrepBank · পাতা ৮ / ১১ · ৭০১–৮০০ / ১,০৭৬

৭০১.
A tap can fill a tank in 6 hours. After half the tank is filled another similar tap is opened. What is the total time taken to fill the tank completely?
  1. ক
    ক) 3 h 30 m
  2. খ
    খ) 3 h 45 m
  3. গ
    গ) 4 h 30 m
  4. ঘ
    ঘ) 4 h
সঠিক উত্তর: গ
গ) 4 h 30 m
উত্তর
সঠিক উত্তর: গ
গ) 4 h 30 m
গ
ব্যাখ্যা

The tap in 1 hour can fill 1/6 part
After 3 hour, 1/2 of the tank is filled
Two tap in 1 hour can fill 1/3 part

So, two tap can fill 1/3 part in 1 hour
They can fill 1 part of the tap in 3/1 = 3 hour
Thus, can fill 1/2 part of the tap in 3×1/2 = 3/2 = 1 and 1/2 hour = 1 hour 30 minute

Total required time = 3 hour + 1 hour and 30 minute = 4 hour and 30 minute

৭০২.
The cost of renting a small bus for a trip was Taka X which was to be shared equally by 16 persons. Actually 10 persons availed the trip. How much more Taka will be the cost per person?
  1. ক
    ক) X/6
  2. খ
    খ) X/10
  3. গ
    গ) 3X/40
  4. ঘ
    ঘ) X/16
  5. ঙ
    ঙ) 3X/80
সঠিক উত্তর: ঙ
ঙ) 3X/80
উত্তর
সঠিক উত্তর: ঙ
ঙ) 3X/80
ঙ
ব্যাখ্যা
Question: The cost of renting a small bus for a trip was Taka X which was to be shared equally by 16 persons. Actually 10 persons availed the trip. How much more Taka will be the cost per person?

Solution:
For 16 persons,
Initial cost per person = X/16

For 10 persons
Actual cost per person = X/10

More cost will be  = X/10 - X/16
= (8X - 5X)/80
= 3X/80
৭০৩.
A can finish a work in 5 days and B takes 4 days to do the same work. If the work is increased 8 times, how many days will it take for both of them to finish the work if they work together?
  1. ক
    ক) 10 days
  2. খ
    খ) 15 days
  3. গ
    গ) 20 days
  4. ঘ
    ঘ) 25 days
সঠিক উত্তর: গ
গ) 20 days
উত্তর
সঠিক উত্তর: গ
গ) 20 days
গ
ব্যাখ্যা
Question: A can finish a work in 5 days and B takes 4 days to do the same work. If the work is increased 8 times, how many days will it take for both of them to finish the work if they work together?

Solution:
A 1 দিনে করতে পারে কাজটির = 1/5 অংশ 
B 1 দিনে করতে পারে কাজটির = 1/4 অংশ 

A এবং B  1 দিনে করতে পারে কাজটির = (1/5) + (1/4)অংশ 
= (4 + 5)/20 
= 9/20 

8 গুণ বৃদ্ধিতে  কাজের মোট পরিমাণ = (1 + 8) = 9 গুণ 

9/20 অংশ কাজ করে = ১ দিনে 
1 অংশ কাজ করে = 20/9 দিনে 
9 অংশ কাজ করে = (20 × 9)/9 দিনে 
= 20 দিন
৭০৪.
A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together?
  1. ক
    6 days
  2. খ
    8 days
  3. গ
    10 days
  4. ঘ
    12 days
সঠিক উত্তর: ঘ
12 days
উত্তর
সঠিক উত্তর: ঘ
12 days
ঘ
ব্যাখ্যা
Question: A job can be done by 3 skilled workmen in 20 days or by 5 boys in 30 days. How many days will they take if they work together?

Solution:
3 men's 1 days work = 1/20 and 5 boy's 1 day's work = 1/30
(3 men + 5 boy)'s 1 day's work = (1/20 + 1/30)
= 5/60 = 1/12

∴ 3 men and 5 boys will complete the work in 12 days.
৭০৫.
L can finish a work in  16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.
  1. ক
    48/5 days
  2. খ
    48/7 days
  3. গ
    48/11 days
  4. ঘ
    10 days
সঠিক উত্তর: ক
48/5 days
উত্তর
সঠিক উত্তর: ক
48/5 days
ক
ব্যাখ্যা
Question: L can finish a work in  16 days and M can do the same work in 12 days. With help of N, they did the work in 4 days only. Then, N alone can do the work in how many days.

Solution:
(L + M + N)’s 1 day’s work =1/4
L’s 1 day’s work = 1/16
M’s 1 day’s work = 1/12

Therefore, N’s 1 day’s work 
= 1/4 - (1/16 + 1/12)
= 1/4 - 7/48 = 5/48

 So, N alone can do the work in 48/5 days.
৭০৬.
A takes twice as much times as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in.
  1. ক
    ক) 4 days
  2. খ
    খ) 8 days
  3. গ
    গ) 6 days
  4. ঘ
    ঘ) 12 days
সঠিক উত্তর: গ
গ) 6 days
উত্তর
সঠিক উত্তর: গ
গ) 6 days
গ
ব্যাখ্যা
ধরি  A, B, C  কাজটি করতে  সময়  নেয়  x , x/2 , x/3 দিন 
তারা 1 দিনে করে  যথাক্রমে 1/x , 2/x , 3/x  অংশ কাজ 
   
প্রশ্নমতে ,  
            1/x + 2/x + 3/x = 1/2 
              (1 + 2 + 3)/x = 1/2
               6/x = 1/2 
                x = 12 
B  কাজটি করতে সময় নেয় = 12/2= 6 দিন
৭০৭.
If 8 men can reap 40 acres in 12 days, then how many acres can 30 men reap in 20 days?
  1. ক
    270 acres
  2. খ
    250 acres
  3. গ
    180 acres
  4. ঘ
    230 acres
  5. ঙ
    None of the above
সঠিক উত্তর: খ
250 acres
উত্তর
সঠিক উত্তর: খ
250 acres
খ
ব্যাখ্যা
Question: If 8 men can reap 40 acres in 12 days, then how many acres can 30 men reap in 20 days?

Solution: 
8 men can reap  in 12 days 40 acres
1 man can reap  in 1 day 40/(12 × 8) acres

∴ 30 men reap in 20 days = (40 × 600)/96
= 250 acres
৭০৮.
3 pumps, working 4 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work, to empty the tank in one day?
  1. ক
    ক) 7 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 6 hours
  4. ঘ
    ঘ) 5 hours
সঠিক উত্তর: গ
গ) 6 hours
উত্তর
সঠিক উত্তর: গ
গ) 6 hours
গ
ব্যাখ্যা

We are given that,
3 pumps, working 4 hours a day, can empty a tank in 2 days. Therefore, it means that:
3 pumps take a total of 8 hours to empty the tank.
Hence, 1 pump will take 8 x 3 = 24 hours

As the number of pumps decreases, the time required increases.
So, if 4 pumps work, the time required decreases.
∴ 24/4 = 6hrs. needed to empty the tank in 1 day.

৭০৯.
Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?
  1. ক
    13 days
  2. খ
    14 days
  3. গ
    16 days
  4. ঘ
    15 days
সঠিক উত্তর: ঘ
15 days
উত্তর
সঠিক উত্তর: ঘ
15 days
ঘ
ব্যাখ্যা
Question: Vikas and Mohan working together can complete a work in 6 days. If Vikas alone completes the same work in 10 days, in how many days Mohan alone can complete the same work?

Solution:
Vikas and Mohan together can complete the task in 6 days.
So, in one day, they will complete 1/6 part of the task.

Therefore, (Vikas + Mohan)'s one day work will be = 1/6
Similarly, Vikas's one day work = 1/10
Therefore, Mohan's one day work = 1/6 - 1/10 = (5 - 3)/30 = 2/30 = 1/15

In one day Mohan completes the 1/15 part of the work so he will complete the entire work in 15 days.
৭১০.
A gym offers two membership plans: Tk. 15 per week or Tk. 50 per month. How much does a person save in a year by opting for the monthly plan rather than the weekly plan?
  1. ক
    90 tk
  2. খ
    140 tk
  3. গ
    160 tk
  4. ঘ
    180 tk
সঠিক উত্তর: ঘ
180 tk
উত্তর
সঠিক উত্তর: ঘ
180 tk
ঘ
ব্যাখ্যা
Question: A gym offers two membership plans: Tk. 15 per week or Tk. 50 per month. How much does a person save in a year by opting for the monthly plan rather than the weekly plan?

Solution:
Annual cost with the weekly plan = 52 × 15 = 780 tk
Annual cost with the monthly plan = 12 × 50 = 600 tk

Savings = 780 - 600 = 180 tk
So, a person saves Tk. 180 in a year by opting for the monthly plan instead of the weekly plan.
৭১১.
Musa can do 1/4 of a work in 6 days. In how many days will he complete the work?
  1. ক
    24 days
  2. খ
    12 days
  3. গ
    36 days
  4. ঘ
    15 days
সঠিক উত্তর: ক
24 days
উত্তর
সঠিক উত্তর: ক
24 days
ক
ব্যাখ্যা
Question: Musa can do 1/4 of a work in 6 days. In how many days will he complete the work?

Solution:
Musa can do 1/4 of a work in 6 days.
∴ He will complete the work in = 6 × 4 = 24 days 

∴ Musa will complete the work in 24 days.
৭১২.
Courier charges for packages to a certain destination are Tk. 95 for the first 300 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 165?
  1. ক
    900 grams
  2. খ
    1000 grams
  3. গ
    1150 grams
  4. ঘ
    1190 grams
  5. ঙ
    1200 grams
সঠিক উত্তর: খ
1000 grams
উত্তর
সঠিক উত্তর: খ
1000 grams
খ
ব্যাখ্যা
Question: Courier charges for packages to a certain destination are Tk. 95 for the first 300 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 165?

Solution:
Let
the additional is 100x grams
Additional 100 grams requires Tk.10
∴ Additional 100x grams requires Tk. (10 × 100x)/100 = Tk. 10x

ATQ,
95 + 10x = 165
⇒ 10x = 70
∴ x = 7

∴ The additional weight = 100 × 7 = 700 grams
∴ Total weight will be = 700 + 300 = 1000 grams
৭১৩.
To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is-
  1. ক
    18 days
  2. খ
    24 days
  3. গ
    26 days
  4. ঘ
    32 days
সঠিক উত্তর: খ
24 days
উত্তর
সঠিক উত্তর: খ
24 days
খ
ব্যাখ্যা
Question: To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is-

Solution:
If B does the work in = 3x days
(A + C) will do the same work in x days.

If C does that work in = 2y days
(A + B) will do it in y days.

∴ (1/x) + (1/3x) = 1/10
⇒ 4/3x = 1/10
⇒ 3x = 40
⇒ x = 40/3
Again,
(1/y) + (1/2y) = 1/10
⇒ 3/2y = 1/10
⇒ 2y = 30
⇒ y = 15

Now, (A + B + C)’s 1 day’s work = 1/10
⇒ (1/A) + (1/40) + (1/30) = 1/10
⇒ 1/A = (1/10) − (1/40) − (1/30)
⇒ 1/A = (12 - 3 - 4)/120
⇒ 1/A = 5/120
⇒ 1/A = 1/24

∴ A alone will complete the work in 24 days.
৭১৪.
If 5 men and 2 boys working together can do four times as much work per hour as a man and a boy together, Working capacities of a man and a boy are in the ratio: 
  1. ক
    ক) 3 : 1
  2. খ
    খ) 2 : 1
  3. গ
    গ) 4 : 1
  4. ঘ
    ঘ) 6 : 1
সঠিক উত্তর: খ
খ) 2 : 1
উত্তর
সঠিক উত্তর: খ
খ) 2 : 1
খ
ব্যাখ্যা
Qustion: If 5 men and 2 boys working together can do four times as much work per hour as a man and a boy together, Working capacities of a man and a boy are in the ratio: 

Solution: 
Let
1 man 1 day work = x
1 boy 1 day work = y

Now
5x + 2y = 4(x + y)
5x + 2y = 4x + 4y 
5x - 4x = 4y - 2y 
x = 2y 
x/y = 2/1
x : y = 2 : 1
৭১৫.
A short distance athlete has taken 60 seconds to cover 100 meters. If he makes 30 steps in 9 seconds, how many steps has he taken in that time?
  1. ক
    ক) 130
  2. খ
    খ) 170
  3. গ
    গ) 173
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: ঘ
ঘ) None of these
উত্তর
সঠিক উত্তর: ঘ
ঘ) None of these
ঘ
ব্যাখ্যা

In 9 sec the athlete makes 30 steps
∴ In 60 sec the athlete will make = (30×60)/9 = 200 steps

৭১৬.
If (2 + √x) > 2√x,
Which of these statements cannot be false?
  1. ক
    x < 4
  2. খ
    x < 1
  3. গ
    x < 3
  4. ঘ
    x < 2
  5. ঙ
    x < 5
সঠিক উত্তর: ক
x < 4
উত্তর
সঠিক উত্তর: ক
x < 4
ক
ব্যাখ্যা

Question: If (2 + √x) > 2√x,
Which of these statements cannot be false?

Solution:
2 + √x > 2√x
⇒ 2 > 2√x - √x
⇒ 2 > √x
⇒ 4 > x
∴ x < 4

৭১৭.
A and B undertake to do a piece of work for Tk. 450. A can do it in 20 days and B can do it in 40 days. With the help of C, they finish it in 8 days. How much should C be paid for his contribution?
  1. ক
    Tk. 180
  2. খ
    Tk. 40
  3. গ
    Tk. 120
  4. ঘ
    Tk. 60
  5. ঙ
    Tk. 50
সঠিক উত্তর: ক
Tk. 180
উত্তর
সঠিক উত্তর: ক
Tk. 180
ক
ব্যাখ্যা
Question: A and B undertake to do a piece of work for Tk. 450. A can do it in 20 days and B can do it in 40 days. With the help of C, they finish it in 8 days. How much should C be paid for his contribution?

Solution:
A & B would have done 8/20 & 8/40 of the work respectively in 8 days.
Together they have done 3/5th of the work.
This implies that C has done 2/5th of the work.
Thus, C should be paid 2/5th of the amount i.e. 450 × (2/5) = Tk. 180.
৭১৮.
X can do a piece of work in 40 days. He works at it for 8 days and then Y finishes it in 16 days. How long will they together take to complete the work?
  1. ক
    ক) 13(1/3) days
  2. খ
    খ) 15 days
  3. গ
    গ) 20 days
  4. ঘ
    ঘ) 26 days
  5. ঙ
    ঙ) None of Above
সঠিক উত্তর: ক
ক) 13(1/3) days
উত্তর
সঠিক উত্তর: ক
ক) 13(1/3) days
ক
ব্যাখ্যা

Work done by X in 8 days = 1/40 x 8 = 1/5
Remaining work = 1 - 1/5 = 4/5

Now, 4/5 work is done by Y in 16 days.
Whole work will be done by Y in = 16 x 5/4 = 20 days.
X's 1 day's work = 1/40
Y's 1 day's work = 1/20
(X + Y)'s 1 day's work = 1/40 + 1/20 = 3/40

Hence, X and Y will together complete the work in = 40/3 = 13(1/3) days.

৭১৯.
20 women take 20 minutes to roll 20 breads. How many breads can 400 women roll in 400 minutes?
  1. ক
    ক) 20
  2. খ
    খ) 2000
  3. গ
    গ) 4000
  4. ঘ
    ঘ) 8000
সঠিক উত্তর: ঘ
ঘ) 8000
উত্তর
সঠিক উত্তর: ঘ
ঘ) 8000
ঘ
ব্যাখ্যা

Men = M; Days = D; Time/Hours = T; Work = W
M1D1T1W2 = M2D2T2W1
Note that W2 is on left side and W1 is on right side

∴ 20 women x 20 minutes x ? = 400 women x 400 minutes x 20 chapattis
∴ ? = 8000 breads = Are rolled by 400 women in 400 minutes.

৭২০.
At a certain diner, a hamburger and coleslaw cost $3.95, and a hamburger and french fries cost $4.40. If french fries cost twice as much as coleslaw, how much do french fries cost?
  1. ক
    $0.45
  2. খ
    $0.60
  3. গ
    $0.75
  4. ঘ
    $0.90
সঠিক উত্তর: ঘ
$0.90
উত্তর
সঠিক উত্তর: ঘ
$0.90
ঘ
ব্যাখ্যা
Question: At a certain diner, a hamburger and coleslaw cost $3.95, and a hamburger and french fries cost $4.40. If french fries cost twice as much as coleslaw, how much do french fries cost?

Solution:
Let,
Cost of hamburger = $h
Cost of coleslaw = $c
Cost of fries = $f

h + c = $3.95 ...............(1)
h + f = $4.40 ................(2)
 
french fries cost twice as much as coleslaw
∴ f = 2c
 
Putting the Value of f in equation (2)
h + 2c = $4.40 ..............(3)

From (3) - (1) we get,
c = $0.45
 
∴ f = $0.45 × 2 = $0.90
৭২১.
Alam starts working on a job and works on it for 12 days and completes 40% of the work. Then Babu joins Alam and together they complete the rest of the work in 12 days. How long (in days) will it take Babu to complete the job if he works alone?
  1. ক
    30
  2. খ
    45
  3. গ
    60
  4. ঘ
    None
সঠিক উত্তর: গ
60
উত্তর
সঠিক উত্তর: গ
60
গ
ব্যাখ্যা
Question: Alam starts working on a job and works on it for 12 days and completes 40% of the work. Then Babu joins Alam and together they complete the rest of the work in 12 days. How long (in days) will it take Babu to complete the job if he works alone?

Solution:
Let 
the total work is 100x
Alam starts working on a job and works on it for 12 days and completes 40% of the work.

Remaining work 100x - 40x = 60x

Babu done 20x in 12 days
∴ Babu done 100x in (12 × 100x)/20x days
= 60 days
৭২২.
There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?
  1. ক
    364,500
  2. খ
    396,900
  3. গ
    45,000
  4. ঘ
    360,000
সঠিক উত্তর: ক
364,500
উত্তর
সঠিক উত্তর: ক
364,500
ক
ব্যাখ্যা
Question: There were 36,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold. If a total of 441,000 copies of the novel were sold in all, how many paperback copies were sold?

Solution:
From the time the first paperback copy was sold until the last copy of the novel was sold 9 times as many paperback copies as hardback copies were sold
Let,
x = number of hardback copies sold during this time
∴ 9x = number of paperback copies sold during this time
∴ x + 9x = total number of copies sold DURING THIS TIME PERIOD
 
A total of 441,000 copies of the novel were sold in all
36,000 hardback copies sold BEFORE the paperback version was issued.
So, we get:
36,000 + x + 9x = 441,000
⇒ 36,000 + 10x = 441,000
⇒ 10x = 405,000
∴ x = 40,500

∴ 9x = 9(40,500) = 364,500
∴ 364,500 paperback copies were sold
৭২৩.
A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -
  1. ক
    12 days
  2. খ
    14 days
  3. গ
    16 days
  4. ঘ
    18 days
সঠিক উত্তর: ঘ
18 days
উত্তর
সঠিক উত্তর: ঘ
18 days
ঘ
ব্যাখ্যা
Question: A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -

Solution:
Let, A, B, and C take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively

Now, 
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, A takes = 6 × 3 = 18 days
৭২৪.
A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?
  1. ক
    11 days
  2. খ
    13 days
  3. গ
    20 (3/17) days
  4. ঘ
    25 days
  5. ঙ
    None of these
সঠিক উত্তর: খ
13 days
উত্তর
সঠিক উত্তর: খ
13 days
খ
ব্যাখ্যা

Ratio of times taken by A and B = 100 : 130 = 10 : 13.
Suppose B takes x days to do the work.

Then,
10 : 13 :: 23 : x
=> x = (23 x 13)/10
=> x = 299.
A's 1 day's work = 1/23
B's 1 day's work = 10/299.

(A + B)'s 1 day's work = (1/23 + 10/299)
= 23/299
= 13.
Therefore, A and B together can complete the work in 13 days.

৭২৫.
If 8 workers can finish a job in 24 days, how many days will it take 12 workers to complete the same job, assuming they all work at the same rate? 
  1. ক
    12 days
  2. খ
    16 days
  3. গ
    21 days
  4. ঘ
    18 days
সঠিক উত্তর: খ
16 days
উত্তর
সঠিক উত্তর: খ
16 days
খ
ব্যাখ্যা

Question: If 8 workers can finish a job in 24 days, how many days will it take 12 workers to complete the same job, assuming they all work at the same rate?

Solution:
8 workers can complete the work in 24 days
∴ 1 worker can complete the work in = 8 × 24 days = 192 days

∴ 12 workers can complete the work in = 192/12 days
= 16 days

∴ It will take 12 workers 16 days to complete the same job.

৭২৬.
P is 25% more efficient than Q. How much time will they, working together, take to complete a job which Q alone could have done in 27 days?
  1. ক
    8 days
  2. খ
    15 days
  3. গ
    18 days
  4. ঘ
    12 days
সঠিক উত্তর: ঘ
12 days
উত্তর
সঠিক উত্তর: ঘ
12 days
ঘ
ব্যাখ্যা

Question: P is 25% more efficient than Q. How much time will they, working together, take to complete a job which Q alone could have done in 27 days?

Solution:
P, Q এর থেকে 25% বেশি দক্ষ।
⇒ P : Q = 125 : 100 = 5 : 4

Q এক দিনে কাজ করে = 4 ইউনিট
P এক দিনে কাজ করে = 5 ইউনিট

 মোট কাজ = Q এর দৈনিক কাজ × Q এর দিন
= 4 × 27 = 108 ইউনিট

একসাথে এক দিনে কাজ করে = 5 + 4 = 9 ইউনিট

তাহলে কাজ শেষ করতে সময় লাগবে = 108 ÷ 9 দিন
= 12 দিন

সুতরাং, P এবং Q একত্রে কাজটি শেষ করতে 12 দিন সময় নেবে।

৭২৭.
A and B undertook to do a piece of work for Tk. 4,500. A alone could do it in 8 days and B alone in 12 days. With the assistance of C they finished the work in 4 days. Then C’s share of money is -
  1. ক
    ক) Tk. 950
  2. খ
    খ) Tk. 850
  3. গ
    গ) Tk. 750
  4. ঘ
    ঘ) Tk. 650
সঠিক উত্তর: গ
গ) Tk. 750
উত্তর
সঠিক উত্তর: গ
গ) Tk. 750
গ
ব্যাখ্যা
Time taken by A to do the work = 8 days
Time taken by B to do the work = 12 days
Time taken by A, B and C together to do the work = 4 days

Calculation:
Let the total work be LCM (8, 12, 4).

LCM (8, 12, 4) = 24 unit

In one day A do = 24/8 unit
⇒ 3 unit

In one day B do = 24/12 unit
⇒ 2 unit

In one day A, B and C do = 24/4 unit
⇒ 6 unit

In one day only C do = 6 - (3 + 2)
⇒ 1 unit

The proportion of their shares = A's 1-day work : B's 1-day work : C's 1-day work
⇒ 3 : 2 : 1

According to the question,
Total share = 4500
⇒ 6 unit = 4500
⇒ 1 unit = 750

So, C's share  = Tk. 750

∴ The C’s share of the money is Tk. 750.
৭২৮.
Running at the same constant rate, 5 identical machines can produce a total of 150 bottles per hour. How many bottles could 14 machines produce in 25 minutes?
  1. ক
    ক) 157
  2. খ
    খ) 175
  3. গ
    গ) 185
  4. ঘ
    ঘ) 200
সঠিক উত্তর: খ
খ) 175
উত্তর
সঠিক উত্তর: খ
খ) 175
খ
ব্যাখ্যা
Question: Running at the same constant rate, 5 identical machines can produce a total of 150 bottles per hour. How many bottles could 14 machines produce in 25 minutes?

Solution: 
in 60 minutes 5 machines can produce = 150 bottles 
In 1 minute 1 machine can produce = 150/(60 × 5) bottles
in 14 minutes 25 machines can produce = (150 × 14 × 25)/(60 × 5) bottles = 175 bottles 
৭২৯.
A group of workers can do a piece of work in 24 days. However, as 7 of them were absent, it took them 30 days, to complete the work. How many people actually worked on the job to complete it?
  1. ক
    28
  2. খ
    30
  3. গ
    32
  4. ঘ
    35
  5. ঙ
    36
সঠিক উত্তর: ঘ
35
উত্তর
সঠিক উত্তর: ঘ
35
ঘ
ব্যাখ্যা
Question: A group of workers can do a piece of work in 24 days. However, as 7 of them were absent, it took them 30 days, to complete the work. How many people actually worked on the job to complete it?

Solution:
Let,
the total number of people were working originally = x
When 7 people were absent,
Total present workers were = x - 7

x workers can complete it = 24 days.
∴ 1 workers can complete it = 24x days.
∴ (x - 7) workers can complete it = 24x/(x - 7) days.

ATQ,
24x/(x - 7) = 30
⇒ 4x/(x - 7) = 5
⇒ 5x - 35 = 4x
∴ x = 35
The total number of people were working originally 35.
৭৩০.
A takes 5 days more than B to do a certain job and 9 days more than C, A and B together can do the job in the same time as C, How many days A would take to do it?
  1. ক
    ক) 15
  2. খ
    খ) 10
  3. গ
    গ) 7
  4. ঘ
    ঘ) 8
সঠিক উত্তর: ক
ক) 15
উত্তর
সঠিক উত্তর: ক
ক) 15
ক
ব্যাখ্যা
Suppose 
A takes x days to do the job alone 
B takes (x - 5) days to do the job alone 
C takes (x - 9) days to do the job alone 

Now
⇒(1/x) + {1/(x - 5)} = 1/(x - 9)
⇒{(x - 5) + x}/{x(x - 5)} = 1/(x - 9)
⇒(2x - 5)/x(x - 5) = 1/(x - 9)
⇒(2x - 5)(x - 9) = x(x - 5)
⇒2x2 - 18x - 5x + 45 = x2 - 5x
⇒2x2 - 18x - 5x + 5x + 45 = 0
⇒x2 - 18x + 45 = 0
⇒x2 - 3x - 15x + 45 = 0
⇒x(x - 3) - 15(x - 3) = 0
⇒(x - 3)(x - 15) = 0
   x = 3, 15 
Here 
x ≠ 3
So
x = 15
৭৩১.
A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days required to complete the work is -
  1. ক
    ক) 6(3/5)
  2. খ
    খ) 8(1/2)
  3. গ
    গ) 10(1/5)
  4. ঘ
    ঘ) 13(1/2)
সঠিক উত্তর: গ
গ) 10(1/5)
উত্তর
সঠিক উত্তর: গ
গ) 10(1/5)
গ
ব্যাখ্যা

B's 3 day's work = (1/21) × 3
= 1/7.
Remaining work = 1 - (1/7)
= 6/7.
(A + B)'s 1 day's work
= (1/14) + (1/21)
= 5/42.
Now, 5/42 work is done by A and B in 1 day.
∴ 6/7 work is done by A and B in (42/5) × (6/7)
= 36/5 days.
Hence, total time taken = 3 + (36/5) days
= 10(1/5) days.

৭৩২.
If 40 workers working at 80% efficiency can complete a task in 15 days, how many workers working at 100% efficiency would be needed to complete the same task in 10 days?
  1. ক
    40 workers
  2. খ
    45 workers
  3. গ
    48 workers
  4. ঘ
    50 workers
সঠিক উত্তর: গ
48 workers
উত্তর
সঠিক উত্তর: গ
48 workers
গ
ব্যাখ্যা

Question: If 40 workers working at 80% efficiency can complete a task in 15 days, how many workers working at 100% efficiency would be needed to complete the same task in 10 days?

Solution: 
Case-1: 
W = 40 × 0.8 × 15
= 480

Case-2:
Let the required number of workers be x.
W = x × 1 × 10
480 = 10x
∴ x = 48

৭৩৩.
If 5 - 3x ≤ 14, then what is the value of x?
  1. ক
    (- ∞, 3]
  2. খ
    (- ∞, - 3]
  3. গ
    [- 3, ∞)
  4. ঘ
    [3, ∞)
সঠিক উত্তর: গ
[- 3, ∞)
উত্তর
সঠিক উত্তর: গ
[- 3, ∞)
গ
ব্যাখ্যা

প্রশ্ন: If 5 - 3x ≤ 14, then what is the value of x?

Solution:
5 - 3x ≤ 14
⇒ - 3x ≤ 14 - 5
⇒ - 3x ≤ 9
⇒ 3x ≥ -9 [উভয় পক্ষকে -1 দ্বারা গুণ করলে]
⇒ x ≥ - 9/3
∴ x ≥ - 3

​এই সমাধানটিকে ব্যবধি (interval) আকারে প্রকাশ করলে হয়: [- 3, ∞)
​এখানে তৃতীয় বন্ধনী [ দ্বারা বোঝায় যে - 3 সমাধান সেটের অন্তর্ভুক্ত, এবং ∞ এর পাশে প্রথম বন্ধনী ) বোঝায় যে এটি অসীম পর্যন্ত বিস্তৃত।

৭৩৪.
A man completes 5/8 of a job in 10 days. At this rate, how many more days will it takes him to finish the job?
  1. ক
    ক) 5
  2. খ
    খ) 6
  3. গ
    গ) 7
  4. ঘ
    ঘ) 8
সঠিক উত্তর: খ
খ) 6
উত্তর
সঠিক উত্তর: খ
খ) 6
খ
ব্যাখ্যা

Work done = 5/8
Balance work =(1 - 5/8) = 3/8
Let the required number of days be x.
Then,(5/8 : 3/8)= :: 10 : x ⇔ 5/8 × x = 3/8 × 10
x = 3/8 × 10 × 8/5
⇒ x = 6.

৭৩৫.
A sum of Tk. 312 was divided among 100 boys and girls in such a way that the boy gets Tk. 3.60 and each girl Tk. 2.40, the number of girls is-
  1. ক
    35
  2. খ
    40
  3. গ
    45
  4. ঘ
    50
সঠিক উত্তর: খ
40
উত্তর
সঠিক উত্তর: খ
40
খ
ব্যাখ্যা
Question: A sum of Tk. 312 was divided among 100 boys and girls in such a way that the boy gets Tk. 3.60 and each girl Tk. 2.40, the number of girls is-

Solution:
Let x be the number of boys and y be the number of girls.
∴ x + y = 100 ............... (i)
∴ 3.60x + 2.40y = 312 ................... (ii)
 
(i) × 3.60 - (ii) ⇒
3.60x + 3.60y = 360 
3.60x + 2.40y = 312
_______________________
             1.20y =  48
∴ y = 48/1.20
= 40

∴ Number of girls = 40
৭৩৬.
Roni can walk a certain distance in 40 days when he rests 9 hours a day. How long will it take to walk twice the distance, twice as face and rest twice as long each day?
  1. ক
    ক) 35 days
  2. খ
    খ) 55 days
  3. গ
    গ) 100 days
  4. ঘ
    ঘ) 80 days
সঠিক উত্তর: গ
গ) 100 days
উত্তর
সঠিক উত্তর: গ
গ) 100 days
গ
ব্যাখ্যা

Working hours per day= 24 – 9 = 15 hrs.
So, Total working hours for 40 days = 15 × 40 = 600 hrs.
On doubling the distance, the time required becomes twice but on walking twice as fast, the time required gets halved. Therefore, the two negates each other with respect to time required.

By increasing rest to twice reduces walking hours per day to 24 – (2 × 9) = 6 hrs.
∴ Number of days required to cover twice the distance, at twice speed with twice the rest = 600/6 = 100 days

৭৩৭.
Ruma can paint 70 walls in 14 minutes. Salma can paint 45 walls in 9 minutes. Working together, how many walls can they paint in 35 minutes?
  1. ক
    450 walls
  2. খ
    400 walls
  3. গ
    300 walls
  4. ঘ
    350 walls
সঠিক উত্তর: ঘ
350 walls
উত্তর
সঠিক উত্তর: ঘ
350 walls
ঘ
ব্যাখ্যা

Question: Ruma can paint 70 walls in 14 minutes. Salma can paint 45 walls in 9 minutes. Working together, how many walls can they paint in 35 minutes?

Solution:
Ruma can paint in 1 minute = 70/14 = 5 walls
Salma can paint in 1 minute = 45/9 = 5 walls

∴ Working together they can paint in 1 minute = (5 + 5) = 10 walls

∴ they can paint in 35 minutes = (35 × 10) = 350 walls

৭৩৮.
In a class, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that class?
  1. ক
    ক) 50
  2. খ
    খ) 60
  3. গ
    গ) 70
  4. ঘ
    ঘ) 80
সঠিক উত্তর: খ
খ) 60
উত্তর
সঠিক উত্তর: খ
খ) 60
খ
ব্যাখ্যা
প্রশ্ন: In a class, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that class?

সমাধান:
ধরি,
বেঞ্চ সংখ্যা ক টি

একটি শ্রেণির প্রতি বেঞ্চে ৪ জন করে ছাত্র বসলে ৩ টি বেঞ্চ খালি থাকে।
∴ ছাত্রসংখ্যা= (ক - ৩) × ৪ জন

প্রতি বেঞ্চে ৩ জন করে ছাত্র বসালে ৬ জন ছাত্রকে দাঁড়িয়ে থাকতে হয়।
∴ ছাত্রসংখ্যা = ৩ক + ৬ জন

প্রশ্নমতে,
(ক - ৩) × ৪ = ৩ক + ৬
⇒ ৪ক - ১২ = ৩ক + ৬
∴ ক = ১৮ 

ছাত্রসংখ্যা = (ক - ৩) × ৪ জন
= (১৮ - ৩) × ৪ জন 
= ১৫ × ৪ জন 
= ৬০ জন 
৭৩৯.
A manager has $ 6,000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?
  1. ক
    $ 750
  2. খ
    $ 1,000
  3. গ
    $ 1,200
  4. ঘ
    $ 1,500
সঠিক উত্তর: গ
$ 1,200
উত্তর
সঠিক উত্তর: গ
$ 1,200
গ
ব্যাখ্যা
Question: A manager has $ 6,000 budgeted for raises for 4 full-time and 2 part-time employees. Each of the full-time employees receives the same raise, which is twice the raise that each of the part-time employees receives. What is the amount of the raise that each full-time employee receives?

Solution:
Let each part time employee receive a raise of $ y
Then each full time employee receives a raise of $ 2y
There are 4 full- time employees and 2 part- time employees
The total budget is $6000
So, the equation is
4(2y) + 2y = 6000
⇒ 10y = 6000
∴ y = 600

∴ Raise for each full-time employee = 2y = 2 × 600 = 1200
৭৪০.
A, B and C together can complete a piece of work in 12 days. All the three started working at it together and after 5 days A left. Then B and C together completed the work in 10 more days. A alone could complete the work in-
  1. ক
    36 days
  2. খ
    40 days
  3. গ
    42 days
  4. ঘ
    55 days
সঠিক উত্তর: খ
40 days
উত্তর
সঠিক উত্তর: খ
40 days
খ
ব্যাখ্যা
Question: A, B and C together can complete a piece of work in 12 days. All the three started working at it together and after 5 days A left. Then B and C together completed the work in 10 more days. A alone could complete the work in-

Solution:
(A + B + C) do 1 work in 12 days.

So (A + B + C)'s 1 day work = 1/12 part
∴ (A + B + C)'s 5 day work = 5/12 part

Remaining work = 1 - (5/12) = 7/12 part

(B + C) takes 10 more days to complete 7/12 part.
∴ (B + C)'s 1 day work = 7/120 part

Now A's 1 day work = (A + B + C)'s 1 day work - (B + C)'s 1 day work
= 1/12 - 7/120
= (10 - 7)/120
= 3/120
= 1/40

∴ A does 1/40 work in in 1 day
∴ A alone could complete the work in 40 days
৭৪১.
A fort had food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is -
  1. ক
    ক) 36 days
  2. খ
    খ) 40 days
  3. গ
    গ) 42 days
  4. ঘ
    ঘ) 48 days
সঠিক উত্তর: গ
গ) 42 days
উত্তর
সঠিক উত্তর: গ
গ) 42 days
গ
ব্যাখ্যা
Question: A fort had food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last is -

Solution:
After 10 days, food having for = 45 - 10 = 35 days
After 25 men left, total = 150 - 25 = 125 men

150 men can eat food for 35 days
1 man can eat food for (35 × 150) days
125 men can eat food for (35 × 150)/125 days
= 42 days
৭৪২.
A cement mixture is composed of 3 elements.By weight, ⅓ of the mixture is sand, 3/5 is water and the remaining 12 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds?
  1. ক
    ক) 60
  2. খ
    খ) 80
  3. গ
    গ) 90
  4. ঘ
    ঘ) 180
  5. ঙ
    ঙ) None
সঠিক উত্তর: ঘ
ঘ) 180
উত্তর
সঠিক উত্তর: ঘ
ঘ) 180
ঘ
ব্যাখ্যা
বালু এবং পানির মোট পরিমাণ (১/৩)+(৩/৫)
= (৫+৯)/১৫ = ১৪/১৫ অংশ
শেষে পাথরের পরিমাণ = ১-(১৪/১৫) = ১/১৫ অংশ
১/১৫ অংশ = ১২ পাউন্ড হলে
১ বা সম্পূর্ণ অংশ হবে = ১৫x১২ = ১৮০ পাউন্ড।
৭৪৩.
A can do a piece of work in 24 days. When he had worked for 4 days, B joined him. If the work was finished in 16 days, B can alone finish that work is -
  1. ক
    ক) 20 days
  2. খ
    খ) 30 days
  3. গ
    গ) 36 days
  4. ঘ
    ঘ) 32 days
সঠিক উত্তর: গ
গ) 36 days
উত্তর
সঠিক উত্তর: গ
গ) 36 days
গ
ব্যাখ্যা
Question: A can do a piece of work in 24 days. When he had worked for 4 days, B joined him. If the work was finished in 16 days, B can alone finish that work is -

Solution:
A's 1 day's work = 1/24 part
A's 16 day's work = 16/24 part
= 2/3 part

Remaining work  = 1 - 2/3 = 1/3 part

1/3 part work done by B in 16 - 4 = 12 days
1 part work done by B in 12 × 3 = 36 days
৭৪৪.
A can do a piece of work in 10 days. While B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get TK. 450 for the whole work, how much money C should get from the whole?
  1. ক
    ΤΚ. 150
  2. খ
    TK. 75
  3. গ
    TK. 225
  4. ঘ
    Tk. 200
  5. ঙ
    None of these
সঠিক উত্তর: খ
TK. 75
উত্তর
সঠিক উত্তর: খ
TK. 75
খ
ব্যাখ্যা
Question: A can do a piece of work in 10 days. While B alone can do it in 15 days. They work together for 5 days and the rest of the work is done by C in 2 days. If they get TK. 450 for the whole work, how much money C should get from the whole?

Solution:
A's work of one day is 1/10
B's work of one day is 1/15

A and B's work of 5 days = 5 × (1/10 + 1/15) = 5 × {(3 + 2)/30}
= 5 × (1/6)
= 5/6

Remaining work = (1 - 5/6) = 1/6

The ratio of A, B, C's work = 5/10 : 5/15 : 1/6 = 1/2 : 1/3 : 1/6 = 3 : 2 : 1
∴ C should get = 450 × (1/6) = 75 Taka
৭৪৫.
A takes 5 days more than B to do a certain job and 9 days more than C. A and B together can do the job in the same time as C. How many days  A would take to do it?
  1. ক
    16 days
  2. খ
    15 days
  3. গ
    14 days
  4. ঘ
    12 days
  5. ঙ
    None
সঠিক উত্তর: খ
15 days
উত্তর
সঠিক উত্তর: খ
15 days
খ
ব্যাখ্যা
Question: A takes 5 days more than B to do a certain job and 9 days more than C. A and B together can do the job in the same time as C. How many days  A would take to do it?

Solution:
Let
A takes x days to do the job alone.

Then,
B takes (x - 5) days
C takes (x - 9) days.

ATQ,
(1/x) + {1/(x - 5)} = 1/(x - 9)
⇒ {(x - 5) + x}/x(x - 5) = 1/(x - 9)
⇒ (2x - 5)/(x2 - 5x) = 1/(x - 9)
⇒ (2x - 5)(x - 9) = x2 - 5x
⇒ 2x2 - 18x - 5x + 45 = x2 - 5x
⇒ 2x2 - 23x + 45 - x2 + 5x = 0
⇒ x2 - 18x + 45 = 0
⇒ x2 - 15x - 3x + 45 = 0
⇒ x(x - 15) - 3(x - 15) = 0
⇒ (x - 15)(x - 3) = 0
∴ x = 15 or 3

But x ≠ 3 [because (3 - 5) = - 2 not exist]

∴ A takes 15 days to do the job alone.
৭৪৬.
A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?
  1. ক
    15 days
  2. খ
    16 days
  3. গ
    17 days
  4. ঘ
    18 days
সঠিক উত্তর: ঘ
18 days
উত্তর
সঠিক উত্তর: ঘ
18 days
ঘ
ব্যাখ্যা
Question: A can do a job in 30 days. B alone can do the same job in 20 days. If A starts the work and joined by B after 10 days, in how many days the job will be done?

Solution:
A's one day work = 1/30
A's ten-day work = (1/30) × 10 = 1/3

So the remaining work would be = 1 - 1/3 = 2/3

B's one day work = 1/20
A and B's one day work = 1/30 + 1/20 = (2 + 3)/60 = 5/60 = 1/12

1/12 of the job will be done by them in one day.
So, the remaining job 2/3 will be done in = (2/3) × 12 = 8 days

Therefore, the total number of days required to do the job would be = 10 + 8 = 18 days
৭৪৭.
A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by B is-
  1. ক
    1/3
  2. খ
    1/4
  3. গ
    1/2
  4. ঘ
    2/3
সঠিক উত্তর: ক
1/3
উত্তর
সঠিক উত্তর: ক
1/3
ক
ব্যাখ্যা
Question: A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by B is-

Solution:
A এর 1 দিনের কাজ = 1/6 অংশ
B এর 1 দিনের কাজ = 1/12 অংশ

তারা একত্রে 1 দিনের কাজ = (1/6) + (1/12) 
= (2 + 1)/12
= 3/12
= 1/4

তারা একত্রে 1/4 অংশ কাজ করে = 1 দিনে
তারা 1 বা সম্পূর্ণ অংশ  কাজ করে = 1/(1/4) = 4 দিনে

∴ B এর দ্বারা সম্পূর্ণ কাজের অংশ = 4 × (1/12) = 1/3
৭৪৮.
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is-
  1. ক
    10
  2. খ
    16
  3. গ
    12
  4. ঘ
    14
সঠিক উত্তর: ঘ
14
উত্তর
সঠিক উত্তর: ঘ
14
ঘ
ব্যাখ্যা
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is-

Solution:
Part time in 2 hours = 6/2 = 1/3
Remaining part = (1 - 1/3) = 2/3
∴ (A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21

∴ C's hour's work= {(A + B + C)'s 1 hour's work} - {(A + B)'s 1 hour's work}
= 1/6 - 2/21
= (7 - 4)/42
= 3/42
= 1/14
 
∴ C alone can fill the tank in 14 hours.
৭৪৯.
Mr. Expert can do a job in 8 days and his son can do it 12 days. How many days will it take them to complete the job if they worked together?
  1. ক
    5
  2. খ
    (24/5)
  3. গ
    5.
  4. ঘ
    None
সঠিক উত্তর: খ
(24/5)
উত্তর
সঠিক উত্তর: খ
(24/5)
খ
ব্যাখ্যা
Question: Mr. Expert can do a job in 8 days and his son can do it 12 days. How many days will it take them to complete the job if they worked together?

Solution: 
Mr. Expert 1 দিনে করতে পারে কাজটির = 1/8 অংশ
তার পুত্র 1 দিনে করতে পারে কাজটির = 1/12 অংশ

তারা একত্রে 1 দিনে করতে পারে কাজটির = (1/8) + (1/12) অংশ
= (3 + 2)/24 অংশ
= 5/24 অংশ

তারা একত্রে কাজটির 5/24 অংশ করতে পারে = 1 দিনে
তারা একত্রে কাজটির 1 অংশ করতে পারে = (1 × 24)/5 দিনে
= 24/5 দিনে
৭৫০.
How much will it cost to fence in a field that is 3000 cm long and 600 cm wide with fence that costs Tk. 50 a meter?
  1. ক
    ক) 720 Tk.
  2. খ
    খ) 1800 Tk.
  3. গ
    গ) 9000 Tk.
  4. ঘ
    ঘ) 3600 Tk.
সঠিক উত্তর: ঘ
ঘ) 3600 Tk.
উত্তর
সঠিক উত্তর: ঘ
ঘ) 3600 Tk.
ঘ
ব্যাখ্যা
Question: How much will it cost to fence in a field that is 3000 cm long and 600 cm wide with fence that costs Tk. 50 a meter?

Solution: 
The perimeter of the field is 2(3000 + 600) cm
= 2 × 3600 cm
= 7200 cm
= 72 m

Total cost = 72 × 50 = 3600 Tk. 
৭৫১.
Nehal's regular pay is Tk 25 per hour up to 40 hours. Overtime is twice the payment for regular times. If he was paid Tk 1800, how many hours overtime did he work?
  1. ক
    8 hours.
  2. খ
    10 hours.
  3. গ
    12 hours.
  4. ঘ
    16 hours.
  5. ঙ
    20 hours.
সঠিক উত্তর: ঘ
16 hours.
উত্তর
সঠিক উত্তর: ঘ
16 hours.
ঘ
ব্যাখ্যা
Question: Nehal's regular pay is Tk 25 per hour up to 40 hours. Overtime is twice the payment for regular times. If he was paid Tk 1800, how many hours overtime did he work?

Solution:
Nehal’s regular wage for 40 hours = (25 × 40) = 1000 Taka.
Amount earned from overtime = (1800 - 1000) Taka = 800 Taka.
Since the overtime rate is twice the regular hourly wage,
Total overtime hours worked = 800 ÷ (25 × 2) hours
= 16 hours.
৭৫২.
A team of 2 men and 5 women completed one-fourth of a project in 3 days. After 3 days one woman left the team and one man joined the team. The newly formed team took 2 days to complete another one fourth of the project. How many days will 4 men takes to complete the project alone?
  1. ক
    6
  2. খ
    8
  3. গ
    12
  4. ঘ
    24
  5. ঙ
    None
সঠিক উত্তর: ক
6
উত্তর
সঠিক উত্তর: ক
6
ক
ব্যাখ্যা
Question: A team of 2 men and 5 women completed one-fourth of a project in 3 days. After 3 days one woman left the team and one man joined the team. The newly formed team took 2 days to complete another one fourth of the project. How many days will 4 men takes to complete the project alone?

Solution:
Let efficiency of one man = M
Let efficiency of one woman = W

ATQ,
(2M + 5W) × 3 = 1/4 of work
⇒ 6M + 15W = 1/4  ... (1)

and, (3M + 4W) × 2 = 1/4
⇒ 6M + 8W = 1/4 ...(2)

Subtracting these equations
7W = 0 ⇒ W = 0
Substituting in equation (2)
6M = 1/4
M = 1/24

For 4 men to complete full work, Time taken = 1/(4 × M)
= 1/{4 × (1/24)
= 24/4
= 6
∴ 4 men will take 6 days to complete the project alone.
৭৫৩.
Suppose today is Saturday. What day of the week will it be 65 days from now on?
  1. ক
    ক) Saturday
  2. খ
    খ) Monday
  3. গ
    গ) Sunday
  4. ঘ
    ঘ) Friday
সঠিক উত্তর: গ
গ) Sunday
উত্তর
সঠিক উত্তর: গ
গ) Sunday
গ
ব্যাখ্যা
প্রশ্ন : Suppose today is Saturday. What day of the week will it be 65 days from now on?
সমাধান : 
Each day of the week is repeated after 7 days.
So, after 63 days [on the 64th Day] it will be Saturday.
∴ 65th day will be Sunday.
৭৫৪.
A and B together can complete a task in 12 days. A alone can do it in 20 days. How many days would it take B to do this job alone?
  1. ক
    21 days
  2. খ
    30 days
  3. গ
    27 days
  4. ঘ
    35 days
  5. ঙ
    40 days
সঠিক উত্তর: খ
30 days
উত্তর
সঠিক উত্তর: খ
30 days
খ
ব্যাখ্যা

Question: A and B together can complete a task in 12 days. A alone can do it in 20 days. How many days would it take B to do this job alone?

Solution:
A একা কাজটি করতে পারে = 20 দিনে
∴ A এর একদিনের কাজ = 1/20 অংশ

A ও B একসাথে কাজটি করতে পারে = 12 দিনে
∴ তাদের একদিনের সম্মিলিত কাজ = 1/12 অংশ

B এর একদিনের কাজ = (A ও B এর সম্মিলিত কাজ) − (A এর একা কাজ)
= (1/12) - (1/20)
= (5 - 3)/60 
= 2/60
= 1/30 অংশ

অতএব, B এক দিনে কাজ করে 1/30 অংশ।
∴ B পুরো কাজটি শেষ করবে = 1 ÷ (1/30) = 30 দিনে।

৭৫৫.
P can do a piece of work in 10 days and Q can do the same piece of work in 15days. P and Q together complete the same piece of work and get Tk. 1000 as the combined wages. Q's share of the wages will be-
  1. ক
    Tk. 600
  2. খ
    Tk. 300
  3. গ
    Tk. 500
  4. ঘ
    Tk. 400
  5. ঙ
    None of these
সঠিক উত্তর: ঘ
Tk. 400
উত্তর
সঠিক উত্তর: ঘ
Tk. 400
ঘ
ব্যাখ্যা
Question: P can do a piece of work in 10 days and Q can do the same piece of work in 15days. P and Q together complete the same piece of work and get Tk. 1000 as the combined wages. Q's share of the wages will be-

Solution:
P এর 1 দিনের কাজ = 1/10
Q এর 1 দিনের কাজ = 1/15

∴ (P + Q) একত্রে 1 দিনের কাজ = (1/10) + (1/15) = (3 + 2)/30 = 5/30 = 1/6

∴ (P + Q) এর 1 দিনের কাজ অনুপাত = (1/10) : (1/15) = 3 : 2

∴ Q এর শেয়ার = {(2/5) × 1000} = 400 টাকা
৭৫৬.
X can complete a piece of work in 18 days, Y in 20 days and Z in 30 days, Y and Z together start the work and forced to leave after 2 days. The time taken by X alone to complete the remaining work is:
  1. ক
    8 days
  2. খ
    12 days
  3. গ
    15 days
  4. ঘ
    10 days
সঠিক উত্তর: গ
15 days
উত্তর
সঠিক উত্তর: গ
15 days
গ
ব্যাখ্যা
Question: X can complete a piece of work in 18 days, Y in 20 days and Z in 30 days, Y and Z together start the work and forced to leave after 2 days. The time taken by X alone to complete the remaining work is:

Solution:
(Y + Z) 2 day's work:
= 2 × (1/20) + (1/30)
= 2 × (3 + 2)/60
= 1/6 part

Remaining work = 1 - (1/6)
= 5/6 part

X's one day's work = 1/18 part

Time taken to complete the work = (5/6)/(1/18) days

∴ Time taken to complete the work = (5/6) × 18
= 15 days
৭৫৭.
Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 8 hours. Another pipe alone can fill two tanks in - 
  1. ক
    28 hours
  2. খ
    48 hours
  3. গ
    44 hours
  4. ঘ
    56 hours
সঠিক উত্তর: খ
48 hours
উত্তর
সঠিক উত্তর: খ
48 hours
খ
ব্যাখ্যা

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 8 hours. Another pipe alone can fill two tanks in - 

Solution: 
Let, the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/8 + 1/X
= (X + 8)/8X

ATQ,
⇒ 8X/(X + 8) = 6
⇒ 8X = 6 × (X + 8) hours.
⇒ 2X = 48
⇒ X = 24

∴ to fill two tanks it will take = 48 hours

৭৫৮.
4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours?
  1. ক
    ক) 17 men
  2. খ
    খ) 14 men
  3. গ
    গ) 13 men
  4. ঘ
    ঘ) 16 men
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: খ
খ) 14 men
উত্তর
সঠিক উত্তর: খ
খ) 14 men
খ
ব্যাখ্যা

4 men can repair a road in 7 hours
1 men can repair a road in 7 × 4hours = 28 hours
28 hours is required by 1 men
2 hours is required by 28/2 men = 14 men

৭৫৯.
A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -
  1. ক
    ক) 18 days
  2. খ
    খ) 12 days
  3. গ
    গ) 9 days
  4. ঘ
    ঘ) 6 days
সঠিক উত্তর: ক
ক) 18 days
উত্তর
সঠিক উত্তর: ক
ক) 18 days
ক
ব্যাখ্যা
Question: A takes twice as much as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 3 days. A can do the work alone in -

Solution:
Let, A, B, and C take 6x, 6x/2 = 3x, and 6x/3 = 2x respectively

Now, 
(1/6x) + (1/3x) + (1/2x) = 1/3
⇒ 6/6x = 1/3
⇒ 1/x = 1/3
⇒ x = 3

So, A takes = 6 × 3 = 18 days
৭৬০.
Rakin's regular pay is 30 Taka per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid 1680 Taka, how many hours of overtime did Rakin work?
  1. ক
    ক) 5 hr
  2. খ
    খ) 6 hr
  3. গ
    গ) 8 hr
  4. ঘ
    ঘ) 10 hr
সঠিক উত্তর: গ
গ) 8 hr
উত্তর
সঠিক উত্তর: গ
গ) 8 hr
গ
ব্যাখ্যা
Question: Rakin's regular pay is 30 Taka per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid 1680 Taka, how many hours of overtime did Rakin work?

Solution:
40 ঘন্টার জন্য রাকিনের নিয়মিত বেতন = (30 × 40) = 1200 টাকা।
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
যেহেতু, Overtime এর প্রতিদিনের টাকার পরিমান নিয়মিত বেতন এর দ্বিগুন,
সেহেতু মোট overtime কাজ করার সময় = 480 ÷ (30×2) ঘন্টা = 8 ঘন্টা।
৭৬১.
P, Q and R can do work in 20 , 30 and 60 days respectively. How many days does it take to complete the work if P does the work and he is assisted by Q and R on every third day?
  1. ক
    15 days
  2. খ
    9 days
  3. গ
    10 days
  4. ঘ
    14 days
  5. ঙ
    18 days
সঠিক উত্তর: ক
15 days
উত্তর
সঠিক উত্তর: ক
15 days
ক
ব্যাখ্যা

Amount of work P can do in 1 day = 1/ 20
Amount of work Q can do in 1 day = 1/ 30
Amount of work R can do in 1 day = 1 /60
P is working alone and every third day Q and R is helping him.

Work completed in every three days = 3 × 1/20 + 1/30 + 1/60 = 1/5
So, work completed in 15 days = 5 × 1/5 = 1
That is, the work will be done in 15 days

৭৬২.
A can complete a work in 12 days, and B can do the same work in 18 days. If they work together for 3 days, what fraction of the work is left?
  1. ক
    5/12 part
  2. খ
    4/11 part
  3. গ
    3/11 part
  4. ঘ
    7/12 part
সঠিক উত্তর: ঘ
7/12 part
উত্তর
সঠিক উত্তর: ঘ
7/12 part
ঘ
ব্যাখ্যা
Question: A can complete a work in 12 days, and B can do the same work in 18 days. If they work together for 3 days, what fraction of the work is left?

Solution:
Given,
A can do the work in 12 days 
A’s 1 day work = 1/12 part

B can do the work in 18 days
B’s 1 day work = 1/18 part

A and B's 1 day work = (1/12 + 1/18) part
= (3 + 2)/36 part
= 5/36 part

∴ Work done in 3 days = {(5/36) × 3} part
= 5/12 part

∴ Remaining work = (1 - 5/12) part
= 7/12 part
৭৬৩.
P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?
  1. ক
    8
  2. খ
    6
  3. গ
    12
  4. ঘ
    4
সঠিক উত্তর: খ
6
উত্তর
সঠিক উত্তর: খ
6
খ
ব্যাখ্যা
Question: P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?

Solution:
P's 1 day's work = 1/(x + 3) part
Q's 1 day's work = 1/(x + 12) part
and (P + Q)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x
⇒ (2x + 15)/(x2 + 15x + 36) = 1/x
⇒ 2x2 + 15x = x2 + 15x + 36
⇒ 2x2 + 15x - x2 - 15x = 36
⇒ x2 = 36
∴ x = 6
৭৬৪.
If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?
  1. ক
    1480 chairs
  2. খ
    1380 chairs
  3. গ
    1320 chairs
  4. ঘ
    1410 chairs
সঠিক উত্তর: খ
1380 chairs
উত্তর
সঠিক উত্তর: খ
1380 chairs
খ
ব্যাখ্যা
Question: If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?

Solution: 
12 carpenters, working 6 hours for 24 days makes (12 × 6 × 24) or, 1728 working hours.
18 carpenters working 8 hours for 36 days makes (18 × 8 × 36) or, 5184 working hours.

1728 working hours = 460 chairs
∴ 5184 working hours = ( 460 × 5184 ) / 1728 chairs
= 1380 chairs
৭৬৫.
Karim completes one-fourth of a piece of work in 4 hours. Rahim works at three times Karim’s speed and finishes the remaining portion of the work. How many hours does Rahim take to complete it?
  1. ক
    3 hours
  2. খ
    4 hours
  3. গ
    2 hours
  4. ঘ
    5 hours
সঠিক উত্তর: খ
4 hours
উত্তর
সঠিক উত্তর: খ
4 hours
খ
ব্যাখ্যা

Question: Karim completes one-fourth of a piece of work in 4 hours. Rahim works at three times Karim’s speed and finishes the remaining portion of the work. How many hours does Rahim take to complete it?

Solution:
Let, Whole work = 1
Karim completes one-fourth (1/4) of a piece of work in 4 hours
∴ Karim’s rate = (1/4)/4 = 1/16 per hour.

∴ Rahim works at three times Karim’s speed
∴ Rahim’s rate = 3 × 1/16 = 3/16 per hour.
∴ Remaining work = (1 - 1/4) = 3/4
∴ Rahim complets 3/4 part work in = (3/4) × (16/3)
= 4 hours

৭৬৬.
5 men and 2 boys working together can do four times as much as work as a man and a boy. Working capacities of a man and a boy are in the ratio -
  1. ক
    ক) 1 : 2
  2. খ
    খ) 2 : 1
  3. গ
    গ) 1 : 3
  4. ঘ
    ঘ) 3 : 1
সঠিক উত্তর: খ
খ) 2 : 1
উত্তর
সঠিক উত্তর: খ
খ) 2 : 1
খ
ব্যাখ্যা
Question: 5 men and 2 boys working together can do four times as much as work as a man and a boy. Working capacities of a man and a boy are in the ratio -

Solution:
Let, 1 man's 1 days's work = x
and 1 boy's 1 day's work = y

ATQ,
5x + 2y = 4(x + y)
⇒ 5x + 2y = 4x + 4y
⇒ x = 2y
⇒ x/y = 2/1
⇒ x : y = 2 : 1
৭৬৭.
A man can do a work in 20 days and a woman in 15 days. If they work on it together for 6 days, then the fraction of the work that is left is-
  1. ক
    1/10
  2. খ
    1/12
  3. গ
    3/10
  4. ঘ
    7/10
  5. ঙ
    7/12
সঠিক উত্তর: গ
3/10
উত্তর
সঠিক উত্তর: গ
3/10
গ
ব্যাখ্যা
Question: A man can do a work in 20 days and a woman in 15 days. If they work on it together for 6 days, then the fraction of the work that is left is-

Solution:
Man’s 1 day’s work = 1/20
Woman’s 1 day’s work = 1/15

(Man + woman)’s 1 day’s work = (1/20 + 1/15)  = 7/60
(Man + woman)’s 6 day’s work = (7/60 × 6) = 7/10

Thus, Remaining work = 1 - 7/10 = 3/10
৭৬৮.
A can do a work in 15 days, and B in 25 days. They work together for 5 days. How much of the work is left?
  1. ক
    1/3
  2. খ
    7/15
  3. গ
    3/10
  4. ঘ
    5/8
সঠিক উত্তর: খ
7/15
উত্তর
সঠিক উত্তর: খ
7/15
খ
ব্যাখ্যা

Question: A can do a work in 15 days, and B in 25 days. They work together for 5 days. How much of the work is left?

Solution:
A, 15 দিনে করতে পারে কাজটির 1 অংশ
A, 1 দিনে করতে পারে কাজটির 1/15 অংশ

B, 25 দিনে করতে পারে কাজটির 1 অংশ
B, 1 দিনে করতে পারে কাজটির 1/25 অংশ

A ও B 1 দিনে করতে পারে কাজটির = (1/15) + (1/25) অংশ
= (5 + 3)/75 অংশ
= 8/75 অংশ

A ও B 5 দিনে করতে পারে কাজটির (5 × 8)/75 অংশ
= 8/15 অংশ

∴ কাজ বাকি থাকে = 1 - 8/15 অংশ
= (15 - 8)/15 অংশ
= 7/15 অংশ

৭৬৯.
It is between 3 pm and 4 pm and the distance between the hour hand and the minute hand of clock is 18 minutes spaces. What time does the clock show ?
  1. ক
    3 : 36 pm
  2. খ
    3 : 21 pm
  3. গ
    3 : 12 pm
  4. ঘ
    3 : 24 pm
সঠিক উত্তর: ক
3 : 36 pm
উত্তর
সঠিক উত্তর: ক
3 : 36 pm
ক
ব্যাখ্যা
Question: It is between 3 pm and 4 pm and the distance between the hour hand and the minute hand of clock is 18 minutes spaces. What time does the clock show?

Solution:
At 3 o'clock, the minute hand is 15 minute spaces behind the hour hand.
Thus, the minute hand has to gain (15 + 18) = 33 minute spaces
55 minutes are gained in 60 minutes.
33 minutes are gained in = (60/55) × 33 minutes
= 36 minutes

∴ The hands will be 18 minutes spaces apart at 3 : 36 pm.
৭৭০.
If I would have been twice as efficient as today, I would have finished work in 12 days. If my efficiency is reduced to one-third of what it is at present, in how many days, I would be able to finish the work?
  1. ক
    18
  2. খ
    8
  3. গ
    52
  4. ঘ
    72
সঠিক উত্তর: ঘ
72
উত্তর
সঠিক উত্তর: ঘ
72
ঘ
ব্যাখ্যা
Question: If I would have been twice as efficient as today, I would have finished work in 12 days. If my efficiency is reduced to one-third of what it is at present, in how many days, I would be able to finish the work?

Solution:
Let I finish work in x days.
With double efficiency, the time taken = x/2 days
That means when the efficiency was double (2x),
then the time taken to finish the work is 12 days
Now,
with the present efficiency time taken to complete the work = 12 × 2 =24 days
With one-third efficiency, the days required to finish the work = 3 × 24 = 72 days,
as efficiency is inversely proportional to days.
Hence, when the efficiency gets one-third, then the work will be finished in 72 days.
৭৭১.
50 people consume 350 kg of rice in 30 days. In how many days will 35 people consume 50 kg of rice?
  1. ক
    ক) 6
  2. খ
    খ) 8
  3. গ
    গ) 12
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: ঘ
ঘ) None of these
উত্তর
সঠিক উত্তর: ঘ
ঘ) None of these
ঘ
ব্যাখ্যা
Let the required number of days be x
Less people, More days (Indirect proportion)
Less quantity, Less days ( Direct proportion)
     People 35 : 50
                            ⟩ :: 30 : x
Quantity 350 : 50
⇒ 35 × 350 × x = 50 × 50 × 30 
⇒ x = 300/49
৭৭২.
X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?
  1. ক
    10 days
  2. খ
    12 days
  3. গ
    15 days
  4. ঘ
    16 days
সঠিক উত্তর: ক
10 days
উত্তর
সঠিক উত্তর: ক
10 days
ক
ব্যাখ্যা
Question: X and Y can do a piece of work in 20 days and 12 days respectively. X started the work alone and then after 4 days Y joined him till the completion of the work. How long did the work last?

Solution:
work done by X in 4 days = (1/20) × 4
= 1/5

∴ Remaining work = 1 - (1/5)
= 4/5

(X + Y)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now,
2/15 work is done by X and Y in 1 day.
So, 4/5 work will be done by X and Y in = (15/2) × (4/5)
= 6 days

Hence, total time taken = (6 + 4) days
= 10 days
৭৭৩.
A fort has enough food for 180 soldiers for 60 days. After 20 days, 60 soldiers leave. For how many more days will the remaining food last
  1. ক
    40
  2. খ
    50
  3. গ
    60
  4. ঘ
    20
সঠিক উত্তর: গ
60
উত্তর
সঠিক উত্তর: গ
60
গ
ব্যাখ্যা
Question: A fort has enough food for 180 soldiers for 60 days. After 20 days, 60 soldiers leave. For how many more days will the remaining food last-

Solution:
After 20 days: 180 soldiers had food for 40 days. Suppose 120 soldiers had food for x days.
Now, fewer soldiers, more days (Indirect Proportion):
120 : 180 : : 40 : x
⇒ 120/180 = 40/x
⇒ 120x = 180 × 40
⇒ x = (180 × 40)/120
∴ x = 60
৭৭৪.
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the smaller wheel has made 21 revolutions, then the number of revolutions made by the larger wheel is:
  1. ক
    ক) 8
  2. খ
    খ) 9
  3. গ
    গ) 10
  4. ঘ
    ঘ) 11
সঠিক উত্তর: খ
খ) 9
উত্তর
সঠিক উত্তর: খ
খ) 9
খ
ব্যাখ্যা

Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x
or, 14 x x = 6 x 21
or, x = (6 x 21)/14
so, x = 9.

৭৭৫.
A assigns B to do a task in 3 days. After 3 days A finds that 3/5 of the work has been done. How many days will B take to complete the rest of the work?
  1. ক
    ক) 5 days
  2. খ
    খ) 2 days
  3. গ
    গ) 3 days
  4. ঘ
    ঘ) 4 days
সঠিক উত্তর: খ
খ) 2 days
উত্তর
সঠিক উত্তর: খ
খ) 2 days
খ
ব্যাখ্যা
Question: A assigns B to do a task in 3 days. After 3 days A finds that 3/5 of the work has been done. How many days will B take to complete the rest of the work?

Solution: 
B ৩/৫ অংশ কাজ করে ৩ দিনে।
সম্পূর্ণ কাজ করে ৩/(৩/৫) দিনে
= ৫ দিনে।

অর্থাৎ B এর সম্পূর্ণ কাজ শেষ করতে আরো (৫ - ৩) বা, ২ দিন লাগবে।
৭৭৬.
A tank can be filled with water by two pipes A and B together in 36 minutes. If the pipe B was stopped after 30 minutes, the tank is filled in 40 minutes. The pipe B can alone fill the tank in:
  1. ক
    ক) 90 minutes
  2. খ
    খ) 91 minutes
  3. গ
    গ) 92 minutes
  4. ঘ
    ঘ) 95 minutes
সঠিক উত্তর: ক
ক) 90 minutes
উত্তর
সঠিক উত্তর: ক
ক) 90 minutes
ক
ব্যাখ্যা
Let the pipes fill the tank in x minutes.
Part of tank filled by pipes A and B in one minute:
1/36 Part of the tank filled by pipe A in 1 minute = 1/36−1/x
According to the question,
30×1/x + 40(1/36−1/x) = 1
⇒30/x + 40/36 − 40/x = 1
⇒30/x + 10/9 − 40/x = 1
⇒10/x = 1/9
Hence, x = 90 minutes.
৭৭৭.
A alone can do a work of Tk. 1200 in 6 days. By engaging an assistant, the work is completed in just 4 days. The share the assistant would receive is -
  1. ক
    ক) 800Tk.
  2. খ
    খ) 400Tk.
  3. গ
    গ) 300Tk.
  4. ঘ
    ঘ) 600Tk.
সঠিক উত্তর: খ
খ) 400Tk.
উত্তর
সঠিক উত্তর: খ
খ) 400Tk.
খ
ব্যাখ্যা
Question: A alone can do a work of Tk. 1200 in 6 days. By engaging an assistant, the work is completed in just 4 days. The share the assistant would receive is - 

Solution: 
A alone can do the work in 6 days
in 1 day,
A can do 1/6 
both can do 1/4
the assistant can do (1/4) - (1/6)
= (3 - 2)/12
= 1/12

So
A : Assistant = 1/6 : 1/12 = 2 : 1

Hence, the share of the assistant is (1200 × 1/3)
= 400 Tk.
৭৭৮.
Mehedi's investment doubles in every 4 years. If he invested Tk. 6000 in each of the years 2014, 2018, 2022 then what will be the amount received by him in 2026?
  1. ক
    42000 Taka
  2. খ
    48000 Taka
  3. গ
    84000 Taka
  4. ঘ
    90000 Taka
সঠিক উত্তর: গ
84000 Taka
উত্তর
সঠিক উত্তর: গ
84000 Taka
গ
ব্যাখ্যা
Question: Mehedi's investment doubles in every 4 years. If he invested Tk. 6000 in each of the years 2014, 2018, 2022 then what will be the amount received by him in 2026?

Solution:
Given,
Investment doubles every 4 years.
He invested Tk. 6000 in each of the years 2014, 2018, 2022.

In 2014 he invested 6000 taka 
In (2014 + 4) = 2018 his investment turned (6000 × 2) = 12000 Taka 

∴ In 2018 after invested another 6000 taka, total investment was (12000 + 6000) = 18000 taka
In (2018 + 4) = 2022 his investment turned (18000 × 2) = 36000 Taka

∴ In 2022 after invested another 6000 taka, total investment was (36000 + 6000) = 42000 taka
In (2022 + 4) = 2026 his investment will be (42000 × 2) = 84000 Taka.

∴ In 2026 he will receive 84000 Taka.
৭৭৯.
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
  1. ক
    20
  2. খ
    30
  3. গ
    40
  4. ঘ
    50
সঠিক উত্তর: খ
30
উত্তর
সঠিক উত্তর: খ
30
খ
ব্যাখ্যা
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

Solution:
Camp has = 200 children
Already have taken meal  = 150 children

Remaining children to take meal = 200 - 150 = 50 children

the camp has meal for 200 children = 120 men
the camp has meal for 1 children = 120/200 men
the camp has meal for 50 children = (120 × 50)/200 men
= 30 men
৭৮০.
A worker’s regular pay is Tk. 20 per hour up to 40 hours. Overtime is paid at 1.5 times the regular rate. If he was paid Tk. 1,100, how many hours of overtime did he work?
  1. ক
    5 hours
  2. খ
    8.5 hours
  3. গ
    10 hours
  4. ঘ
    13 hours
সঠিক উত্তর: গ
10 hours
উত্তর
সঠিক উত্তর: গ
10 hours
গ
ব্যাখ্যা

Question: A worker’s regular pay is Tk. 20 per hour up to 40 hours. Overtime is paid at 1.5 times the regular rate. If he was paid Tk. 1,100, how many hours of overtime did he work?

Solution:
ধরি, তিনি x ঘণ্টা overtime কাজ করেছেন।

সাধারণ বেতন (40 ঘণ্টার জন্য) = 20 × 40 = 800 টাকা
Overtime হার (প্রতি ঘণ্টা) = 20 × 1.5 = 30 টাকা
Overtime বেতন = 30 × x = 30x টাকা

মোট বেতন = সাধারণ বেতন + overtime বেতন
শর্তমতে,
800 + 30x = 1,100
⇒ 30x = 1,100 - 800
⇒ 30x = 300
⇒ x = 300 / 30
∴ x = 10

∴ তিনি 10 ঘণ্টা overtime করেছেন।

৭৮১.
Asif can copy 50 pages in 10 hours; Asif and Tamim together can copy 300 pages in 40 hours. In how much time(hour) can Tamim copy 30 pages?
  1. ক
    9
  2. খ
    10
  3. গ
    11
  4. ঘ
    12
  5. ঙ
    13
সঠিক উত্তর: ঘ
12
উত্তর
সঠিক উত্তর: ঘ
12
ঘ
ব্যাখ্যা
Number of page copied by (Asif and Tamim) in 1 hour = 300/40 = 7.5 pages;
Asif copied pages in one hour = 50/10 = 5 pages
Hence, Tamim copied pages in one hour = 7.5 - 5 = 2.5 pages
Thus, Tamim can copy 30 pages in  30/2.5 hours or 12 hours
৭৮২.
A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?
  1. ক
    7:00 a.m.
  2. খ
    2:00 a.m.
  3. গ
    6:00 a.m.
  4. ঘ
    9:00 a.m.
  5. ঙ
    4:00 a.m.
সঠিক উত্তর: ঘ
9:00 a.m.
উত্তর
সঠিক উত্তর: ঘ
9:00 a.m.
ঘ
ব্যাখ্যা
Question: A certain culture of bacteria quadruples every hour. If a container with these bacteria was half full at 10:00 a.m., at what time was it one-eighth full?

Solution:
At 10:00 a.m., the container is half full
The bacteria quadruple (multiply by 4) every hour

From half full (1/2), we want to find when the container was one-eighth full (1/8)
Let's work backwards by dividing by 4 at each step
10:00 a.m.: 1/2 full
9:00 a.m.: (1/2) ÷ 4 = 1/8 full
At 9:00 a.m., the container is 1/8 full
৭৮৩.
Emon takes twice as much time as Rayhan to complete a work and Hemel does it in the same time as Emon and Rayhan together. If all three working together can finish the work in 9 days, then the time taken by Emon to finish the work is-
  1. ক
    50 days
  2. খ
    54 days
  3. গ
    62 days
  4. ঘ
    66 days
সঠিক উত্তর: খ
54 days
উত্তর
সঠিক উত্তর: খ
54 days
খ
ব্যাখ্যা
Question: Emon takes twice as much time as Rayhan to complete a work and Hemel does it in the same time as Emon and Rayhan together. If all three working together can finish the work in 9 days, then the time taken by Emon to finish the work is-

Solution:
Let,
Rayhan takes x days to complete a work
Then, Emon takes 2x days to complete the work

Rayhan's 1 day's work = 1/x
Emon's 1 day's work = 1/2x
Hemel's 1 day's work = (1/x) + (1/2x) = 3/2x

∴ (Emon + Rayhan + Hemel)'s 1 day's work
= (1/x) + (1/2x) + (3/2x)
= (2 + 1 + 3)/2x
= 3/x

ATQ,
3/x = 1/9
⇒ x = 27

Hence, Emon takes (2 × 27) = 54 days to complete the work.
৭৮৪.
If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?
  1. ক
    240 mats
  2. খ
    245 mats
  3. গ
    250 mats
  4. ঘ
    260 mats
সঠিক উত্তর: ঘ
260 mats
উত্তর
সঠিক উত্তর: ঘ
260 mats
ঘ
ব্যাখ্যা
Question: If 10 men or 20 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 4 boys in 20 days?

Solution:
Here,
10 men = 20 boys
1 men = 2 boys
8 men = (2 × 8) boys
= 16 boys

If 20 boys can make 260 mats in 20 days,
8 men and 4 boys or, (16 + 4) = 20 boys can make in 20 days = 260 mats.
৭৮৫.
If A and B together can complete a work in 24 days, A and C together in 18 days, and B and C together in 12 days, then C alone can do the work in:
  1. ক
    5 days
  2. খ
    8 days
  3. গ
    10 days
  4. ঘ
    None of these
সঠিক উত্তর: ঘ
None of these
উত্তর
সঠিক উত্তর: ঘ
None of these
ঘ
ব্যাখ্যা
A and B together can complete a work in 24 day
A and B together can complete 1/24 portion of a work in 1 day

A and C together can complete a work in 18 day
A and C together can complete 1/18 portion of a work in 1 day

B and C together can complete 1/12 portion of a work in 1 day

A, B and C together can complete (1/24 + 1/18 + 1/12)/2 or 13/144 portion of a work in 1 day
one day's work of C = (13/144 - 1/24) or 7/144 portion
C can complete 7/144 portion in 1 day
C alone can do the work in 144/7 days or 20.57 days or 21 days
৭৮৬.
Soma did 3/5 of a work in 9 days. The rest of the work is done in -
  1. ক
    ক) 7 days
  2. খ
    খ) 6 days
  3. গ
    গ) 5 days
  4. ঘ
    ঘ) 4 days
সঠিক উত্তর: খ
খ) 6 days
উত্তর
সঠিক উত্তর: খ
খ) 6 days
খ
ব্যাখ্যা
Question: Soma did 3/5 of a work in 9 days. The rest of the work is done in - 

Solution: 
3/5 of a work is done within 9 days.
so, the total work is done in (9 × 5)/3 = 15 days.

hence, rest of the work is done in (15 - 9) or, 6 days
৭৮৭.
A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?
  1. ক
    ক) 1 day
  2. খ
    খ) 2 days
  3. গ
    গ) 3 days
  4. ঘ
    ঘ) 4 days
সঠিক উত্তর: ক
ক) 1 day
উত্তর
সঠিক উত্তর: ক
ক) 1 day
ক
ব্যাখ্যা
Question: A carrier can carry 1.5 tons of products in 1 day from Teknaf to Tetulia. How much time will it be required to transfer 3 tons in two carriers?

Solution: 
১ টি কেরিয়ার ১.৫ টন মাল বহন করতে সময় নেয় ১ দিন
২ টি কেরিয়ার ৩ টন মাল বহন করতে সময় নেয় = (১.৫ × ২)/৩ = ১ দিন
৭৮৮.
A can finish a piece of work in 18 days and B can do the same work in half of the time taken by A. Then working together what part of the same work they can finish in a day?
  1. ক
    ক) 1/6
  2. খ
    খ) 2/5
  3. গ
    গ) 1/9
  4. ঘ
    ঘ) 2/7
সঠিক উত্তর: ক
ক) 1/6
উত্তর
সঠিক উত্তর: ক
ক) 1/6
ক
ব্যাখ্যা

A's 1 day work = 1/18
B's 1 day work = 1/9 [because B take half time than A]
So, (A + B)'s one day work
= 1/18 + 1/9
= (1+2)/18
= 1/6

৭৮৯.
Bimol takes twice as much time as Rakib to complete a work and Alfi does it in the same time as Bimol and Rakib together. If all three working together can finish the work in 9 days, then the time taken by Bimol to finish the work is-
  1. ক
    62 days
  2. খ
    52 days
  3. গ
    48 days
  4. ঘ
    54 days
  5. ঙ
    None of these
সঠিক উত্তর: ঘ
54 days
উত্তর
সঠিক উত্তর: ঘ
54 days
ঘ
ব্যাখ্যা

Question: Bimol takes twice as much time as Rakib to complete a work and Alfi does it in the same time as Bimol and Rakib together. If all three working together can finish the work in 9 days, then the time taken by Bimol to finish the work is-

Solution:
Let,
Rakib takes x days to complete a work
Then, Bimol takes 2x days to complete the work

Rakib's 1 day's work = 1/x
Bimol's 1 day's work = 1/2x
Alf's 1 day's work = (1/x) + (1/2x) = 3/2x

(Bimol + Rakib + Alfi)'s 1 day's work = (1/x) + (1/2x) + (3/2x)
= (2 + 1 + 3)/2x
= 3/x

ATQ,
3/x = 1/9
⇒ x = 27
Hence, Bimol takes (2 × 27) = 54 days to complete the work.

৭৯০.
8 men can complete a piece of work in 20 days. 8 women can complete the same work in 32 days. In how many days will 5 men and 8 women together complete the same work?
  1. ক
    16 days
  2. খ
    14 days
  3. গ
    12 days
  4. ঘ
    18 days
সঠিক উত্তর: ক
16 days
উত্তর
সঠিক উত্তর: ক
16 days
ক
ব্যাখ্যা

Question: 8 men can complete a piece of work in 20 days. 8 women can complete the same work in 32 days. In how many days will 5 men and 8 women together complete the same work?

Solution:
8 × 20 men = 8 × 32 women
5 men = 8 women
Now, 5 men + 8 women = 8 + 8 = 16 women

ATQ, D1 × M1= M2× D2
⇒ 8 × 32 women = 16 × D2
⇒ D2= (32 × 8)/16
∴ D2= 16 days

৭৯১.
A hostel had provision of food for 150 men for 45 days. After 10 days, 25 men left the hostel. What is the number of days for which the remaining food will last?
  1. ক
    10 days
  2. খ
    20 days
  3. গ
    42 days
  4. ঘ
    45 days
সঠিক উত্তর: গ
42 days
উত্তর
সঠিক উত্তর: গ
42 days
গ
ব্যাখ্যা
Remaining days = 45 - 10 = 35
Remaining students = 150 - 25 = 125
For 150 students, there is food for 35 days
For 125 students, there is food for 35×150/125 days or 42 days
৭৯২.
By working 3 hours a day, P can complete a work in 12 days, and working 4 hours a day, Q can complete the same work in 9 days. Working 6 hours a day, they can jointly complete the work in -
  1. ক
    2 days
  2. খ
    3 days
  3. গ
    4 days
  4. ঘ
    5 days
  5. ঙ
    None
সঠিক উত্তর: খ
3 days
উত্তর
সঠিক উত্তর: খ
3 days
খ
ব্যাখ্যা
Question: By working 3 hours a day, P can complete a work in 12 days, and working 4 hours a day, Q can complete the same work in 9 days. Working 6 hours a day, they can jointly complete the work in -

Solution:
P can complete the work in = 3 × 12 = 36 hours
Q can complete the work in = 4 × 9 = 36 hours

(P + Q)'s 1 hour's work = (1/36) + (1/36)
= 2/36
= 1/18

Hence, P and Q can complete the work in 18 hours
So, working 6 hours a day they require = 18/6 = 3 days to complete the work
৭৯৩.
Working 4 hours a day, A can Complete a work in 10 days and working 5 hours a day, B can complete the same work in 12 days. Working 8 hours a day, they can jointly complete the work in:
  1. ক
    ক) 2 days
  2. খ
    খ) 3 days
  3. গ
    গ) 4 days
  4. ঘ
    ঘ) 5 days
সঠিক উত্তর: খ
খ) 3 days
উত্তর
সঠিক উত্তর: খ
খ) 3 days
খ
ব্যাখ্যা
Question : Working 4 hours a day, A can Complete a work in 10 days and working 5 hours a day, B can complete the same work in 12 days. Working 8 hours a day, they can jointly complete the work in:

Solution: 
Working 4 hours a day, A can complete the work in 10 days i.e.
= 4 × 10 = 40 hours
Working 5 hours a day, B can complete the work in 12 days i.e.
= 5 × 12 = 60 hours

(A + B)'s 1 hour's work,
(1/40) + (1/60)
= (6 + 4)/240
= 10/240
= 1/24

Hence, A and B can complete the work in 24 hours 
they require 3 days to complete the work.
৭৯৪.
In a race, the speeds of A and B are in the ratio of 5 : 6. A takes 20 minutes more than B takes to reach the destination. What is the time taken by A to reach the destination in hours?
  1. ক
    1.5 hours
  2. খ
    2 hours
  3. গ
    3 hours
  4. ঘ
    4 hours
সঠিক উত্তর: খ
2 hours
উত্তর
সঠিক উত্তর: খ
2 hours
খ
ব্যাখ্যা
Question: In a race, the speeds of A and B are in the ratio of 5 : 6. A takes 20 minutes more than B takes to reach the destination. What is the time taken by A to reach the destination in hours?

Solution:
Ratio of speeds = 5/6
⇒ Ratio of times taken = 6/5

Let,
A and B take 6x and 5x hours to reach the destination.

ATQ,
6x - 5x = 20/60
∴ x = 1/3

∴ Time taken by A = 6x = (6 × 1/3) hours
= 2 hours.
৭৯৫.
Sumi can type 75 pages in 25 minutes. Maria can type 5 pages in 15 minutes. Working together, how many pages can they type in 30 minutes?
  1. ক
    75 pages
  2. খ
    80 pages
  3. গ
    90 pages
  4. ঘ
    100 pages
  5. ঙ
    105 pages
সঠিক উত্তর: ঘ
100 pages
উত্তর
সঠিক উত্তর: ঘ
100 pages
ঘ
ব্যাখ্যা
Question: Sumi can type 75 pages in 25 minutes. Maria can type 5 pages in 15 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Sumi can type in 1 min = 75/25 = 3 pages
Maria can type in 1 min = 5/15 = 1/3 page

∴ Working together they can type in 1 min = (3 + 1/3) pages
= 10/3 pages

∴ They can type in 30 min = (10 × 30)/3 pages
= 100 pages
৭৯৬.
An empty swimming pool with a capacity of 5,760 gallons is filled at the rate of 12 gallons per minute. How many hours does it take to fill the pool to capacity?
  1. ক
    8
  2. খ
    20
  3. গ
    96
  4. ঘ
    480
  5. ঙ
    720
সঠিক উত্তর: ক
8
উত্তর
সঠিক উত্তর: ক
8
ক
ব্যাখ্যা
Question: An empty swimming pool with a capacity of 5,760 gallons is filled at the rate of 12 gallons per minute. How many hours does it take to fill the pool to capacity?

Solution:
The pool to its capacity of 5,760 gallons.
The "rate of work" is 12 gallons per minute.

Fill in 1 min 12 gallon
Fill in 60 min (12 × 60) = 720 gallon

720 gallon is filled in 1 hour
5,760 gallons filled in (1 × 5760)/720 hours
= 8 hours
৭৯৭.
If 10 men or 15 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 12 boys in 20 days?
  1. ক
    562 mats
  2. খ
    416 mats
  3. গ
    386 mats
  4. ঘ
    360 mats
সঠিক উত্তর: খ
416 mats
উত্তর
সঠিক উত্তর: খ
416 mats
খ
ব্যাখ্যা
Question: If 10 men or 15 boys can make 260 mats in 20 days, then how many mats will be made by 8 men and 12 boys in 20 days?

Solution:
Here
10 men = 15 boys
∴ 1 men = 15/10 boys 
∴ 8 men = (15 × 8)/10 boys
= 12 boys

∴ 8 men and 12 boys = (12 + 12) = 24 boys

15 boys can make in 20 days 260 mats 
∴ 1 boys can make in 20 days 260/15 mats 
∴ 24 boys can make 260 mats in (260 × 24)/15 mats 
= 416 mats 
৭৯৮.
In a camp, there is a meal for 240 men or 400 children. If 300 children have taken the meal, how many men will be catered to with remaining meal?
  1. ক
    40 men
  2. খ
    30 men
  3. গ
    80 men
  4. ঘ
    60 men
সঠিক উত্তর: ঘ
60 men
উত্তর
সঠিক উত্তর: ঘ
60 men
ঘ
ব্যাখ্যা
Question: In a camp, there is a meal for 240 men or 400 children. If 300 children have taken the meal, how many men will be catered to with remaining meal?

Solution:
Camp has = 400 children
Already have taken meal = 300 children

Remaining children to take meal = 400 - 300 = 100 children

the camp has meal for 400 children = 240 men
the camp has meal for 1 children = 240/400 men
the camp has meal for 100 children = (240 × 100)/400 men
= 60 men
৭৯৯.
A can do a piece of work in 24 days, B in 32 days and C in 64 days. All begin to do it together, but A leaves after 6 days and B leaves 6 days before the completion of the work. How many days did the work last?
  1. ক
    ক) 15
  2. খ
    খ) 12
  3. গ
    গ) 17
  4. ঘ
    ঘ) 20
সঠিক উত্তর: ঘ
ঘ) 20
উত্তর
সঠিক উত্তর: ঘ
ঘ) 20
ঘ
ব্যাখ্যা
L.C.M. of 24, 32 and 64 is 192. Hence:
A’ s efficiency = 8
B’s efficiency = 6
C’s efficiency = 3.
In 6 days they produce 17 × 6 = 102 units. (1)
Also given that C works alone for 6 days. Number of units produced by C in those 6 days = 6 × 3 = 18 units (2)
Total (1) + (2) = 120.
Balance units 72 done by Band C :Their 1 days production: 9 units.
Hence they worked for 8 days for producing the 72 units.(3)
Total days of work: 6 + 8 + 6= 20 days.
৮০০.
A contract is to be finished in 46 days and 117 men involved in it, each working 8 hours per day. After 33 days, 4/7 of the work is finished, how many additional men may be employed so that it may be completed in time, each man now working 9 hours a day?
  1. ক
    85
  2. খ
    196
  3. গ
    81
  4. ঘ
    123
সঠিক উত্তর: গ
81
উত্তর
সঠিক উত্তর: গ
81
গ
ব্যাখ্যা
Question: A contract is to be finished in 46 days and 117 men involved in it, each working 8 hours per day. After 33 days, 4/7 of the work is finished, how many additional men may be employed so that it may be completed in time, each man now working 9 hours a day?

Question:
let the total work be W need to be completed in 46 days

117 men working 33 days 8 hours completed 4/7 of W that means 3/7 of W is left.

117 × 33 × 8 = 4W/7 .........(1)

let x men added to complete the 3/7 of W in 13 days (Total 46 days ,33 already over.) working 9 hours.

(117 + x) × 13 × 9 = 3W/7 ...........(2)

dividing (1) and (2)
(117 × 33 × 8)/{(117 + x) × 13 × 9} = (4W/7)/(3W/7)
⇒ 264/(117 + x) = 4/3
⇒ 468 + 4x = 792
⇒ 4x = 324
⇒ x = 324/4
∴ x = 81