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Time & Work, Chain Rule

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

Time & Work, Chain Rule

PrepBank · পাতা ৭ / ১১ · ৬০১–৭০০ / ১,০৭৬

৬০১.
If 2 jackets and 3 sweaters cost Tk. 4,400, and 3 jackets and 2 sweaters cost Tk. 4,700, find the cost of a single jacket. 
  1. ক
    Tk. 1300
  2. খ
    Tk. 1000
  3. গ
    Tk. 1060
  4. ঘ
    Tk. 2400
সঠিক উত্তর: গ
Tk. 1060
উত্তর
সঠিক উত্তর: গ
Tk. 1060
গ
ব্যাখ্যা

Question: If 2 jackets and 3 sweaters cost Tk. 4,400, and 3 jackets and 2 sweaters cost Tk. 4,700, find the cost of a single jacket.

Solution:
ধরি, একটি জ্যাকেটের মূল্য x টাকা এবং একটি সোয়েটারের মূল্য y টাকা।

প্রশ্নমতে,
2x + 3y = 4400 ............... (i) 
3x + 2y = 4700 .............. (ii)

(ii) × 3 - (i) × 2 ⇒
(9x + 6y) - (4x + 6y) = 14100 - 8800
⇒ 9x - 4x = 5300
⇒ 5x = 5300
⇒ x = 5300/5
⇒ x = 1060

সুতরাং, একটি জ্যাকেটের মূল্য 1060 টাকা।

৬০২.
A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his pay of 7th day?
  1. ক
    ক) Tk. 150
  2. খ
    খ) Tk. 140
  3. গ
    গ) Tk. 90
  4. ঘ
    ঘ) Tk. 160
সঠিক উত্তর: ক
ক) Tk. 150
উত্তর
সঠিক উত্তর: ক
ক) Tk. 150
ক
ব্যাখ্যা
Question: A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his pay of 7th day?

Solution:
Let,
The pays of seven days respectively : x, x + 10, x + 20, x + 30, x + 40, x + 50, x + 60 

ATQ,
x + x + 10 + x + 20 + x + 30 = x + 40 + x + 50 + x + 60
⇒ 4x + 60 = 3x + 150
∴ x = 90 

∴ His pay of 7th day is Tk. (90 + 60)
= Tk. 150
৬০৩.
56 men complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?
  1. ক
    ক) 118
  2. খ
    খ) 32
  3. গ
    গ) 48
  4. ঘ
    ঘ) 98
সঠিক উত্তর: খ
খ) 32
উত্তর
সঠিক উত্তর: খ
খ) 32
খ
ব্যাখ্যা

Let,
The required number of days be x.
Less Man, More Days [Indirect proportion]
∴ 42 : 56 :: 24 : x
⇒ 42x = 56 × 24
⇒ x = (56 × 24)/42
⇒ x = 32.

৬০৪.
If 15 men can reap the crops of a field in 28 days, in how many days will 5 men reap it?
  1. ক
    50 days
  2. খ
    60 days
  3. গ
    84 days
  4. ঘ
    9.333 days
সঠিক উত্তর: গ
84 days
উত্তর
সঠিক উত্তর: গ
84 days
গ
ব্যাখ্যা
Question: If 15 men can reap the crops of a field in 28 days, in how many days will 5 men reap it?

Solution:
Let 5 men can reap a field in x days
So, put the same quantities on the same side.
Men: Days
Now, Men and Days are inversely proportional to each other. If we increase the number of men fewer days will be required to complete the work.
Inversely proportional means = 15 = 1/28, 5 = 1/x
so, 5/15 = 28/x
⇒ 5x = 28 × 15
∴ x = 84

Hence, 5 men can reap a field in 84 days.
৬০৫.
A man and a boy received Tk. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?
  1. ক
    ক) Tk. 40
  2. খ
    খ) Tk. 42
  3. গ
    গ) Tk. 48
  4. ঘ
    ঘ) Tk. 56
সঠিক উত্তর: ক
ক) Tk. 40
উত্তর
সঠিক উত্তর: ক
ক) Tk. 40
ক
ব্যাখ্যা
Man = 3 boy
Daily wages for them = 800/5
 = 160
4 boy (1 man + 1 boy) = 160
4 boy = 160
Or, boy = Tk. 40
৬০৬.
It takes 5 hours to fill a container using machine A. The same container can be filled using machine B in 10 hours. When the container is full, Machine C can fully empty the container in 20 hours. If all three machines start working on the same empty container how long will it take for the container to be completely filled,
  1. ক
    ক) 1/2 hours
  2. খ
    খ) 4 hours
  3. গ
    গ) 2 hours
  4. ঘ
    ঘ) 15 hours
সঠিক উত্তর: খ
খ) 4 hours
উত্তর
সঠিক উত্তর: খ
খ) 4 hours
খ
ব্যাখ্যা

3 টি মেশিন দ্বারা 1 ঘণ্টায় পূর্ণ হয় = (1/5 + 1/10 − 1/20)
=  (4 + 2 − 1) / 20 অংশ
= 5 / 20 অংশ
= 1/4 অংশ

মেশিন 3টি দ্বারা = 1/4 অংশ পূর্ণ হয় 1 ঘণ্টায়
∴ 1 বা সম্পূর্ণ অংশ পূর্ণ হয় (1×4) = 4 ঘণ্টায়

৬০৭.
A person travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr, he reaches 15 min earlier. The distance he has to travel is -
  1. ক
    ক) 4.5km
  2. খ
    খ) 6 km
  3. গ
    গ) 7.2 km
  4. ঘ
    ঘ) 12 km
সঠিক উত্তর: খ
খ) 6 km
উত্তর
সঠিক উত্তর: খ
খ) 6 km
খ
ব্যাখ্যা

ATQ,
D/3 - 15/60 = D/4 + 15/60 [As, 60 minutes = 1 hour]
⇒ D/3 - D/4 = 15/60 + 15/60 = 30/60
⇒ D/12 = 1/2
∴ D = 12/2 = 6 km

৬০৮.
A Company employs 20 persons, each working 42 hours a week. If 5 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?
  1. ক
    56 hours
  2. খ
    46 hours
  3. গ
    52 hours
  4. ঘ
    60 hours
সঠিক উত্তর: ক
56 hours
উত্তর
সঠিক উত্তর: ক
56 hours
ক
ব্যাখ্যা
Question: A Company employs 20 persons, each working 42 hours a week. If 5 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?

Solution:
একটি কোম্পানি ২০ জন কর্মচারী নিয়োগ দেয়। প্রত্যেকে ৪২ ঘণ্টা কাজ করে।

∴ মোট কাজ হয় = (২০ × ৪২)
= ৮৪০ ঘণ্টা
৫ জন অনুপস্থিত থাকলে, বাকি থাকে = ২০ - ৫ = ১৫ জন

∴ প্রত্যেকের কাজ করতে হবে ৮৪০/১৫ ঘণ্টা
= ৫৬ ঘণ্টা
৬০৯.
A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work? 
  1. ক
    7 days
  2. খ
    9 days
  3. গ
    12 days
  4. ঘ
    10 days
সঠিক উত্তর: খ
9 days
উত্তর
সঠিক উত্তর: খ
9 days
খ
ব্যাখ্যা

Question: A can complete the work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

Solution:
A একা কাজটি করতে পারে = 24 দিনে
∴ A এর একদিনের কাজ = 1/24 অংশ
এবং, 
   B একা কাজটি করতে পারে = 16 দিনে
∴ B এর একদিনের কাজ = 1/16 অংশ

∴ A ও B একসাথে একদিনের কাজ = (1/24) + (1/16) = (2 + 3)/48 = 5/48 অংশ
তারা 6 দিনে একসাথে কাজ করে = 6 × (5/48) = 5/8 অংশ

বাকি কাজ = 1 - (5/8) = 3/8 অংশ

অতএব,
A, 1/24 অংশ কাজ করে 1 দিনে 
∴ 3/8  অংশ কাজ করে = (24 × 3)/8 = 9 দিনে 

অতএব, A একা বাকি কাজ শেষ করতে 9 দিন লাগবে।

৬১০.
A, B, and C can do a piece of work in 20, 30, and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    ক) 12 days
  2. খ
    খ) 15 days
  3. গ
    গ) 16 days
  4. ঘ
    ঘ) 18 days
সঠিক উত্তর: খ
খ) 15 days
উত্তর
সঠিক উত্তর: খ
খ) 15 days
খ
ব্যাখ্যা

A's 2 day's work = (1/20) × 2
= 1/10
(A + B + C)'s 1 day's work = (1/20) + (1/30) + (1/60)
= 6/60
= 1/10
(A + B + C) work in 3 days = (1/10) + (1/10)
= 1/5.
Now, 1/5 work is done in 3 days.
∴ Whole work is done in (3 × 5)
= 15 days.

৬১১.
A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?
  1. ক
    ক) 10 days
  2. খ
    খ) 15 days
  3. গ
    গ) 18 days
  4. ঘ
    ঘ) 22 days
সঠিক উত্তর: খ
খ) 15 days
উত্তর
সঠিক উত্তর: খ
খ) 15 days
খ
ব্যাখ্যা
Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. If B does the work only for half a day daily, then in how many days A and B together will complete the work?

Solution:
B's 1 day's work = 1/12 - 1/20 = 1/30
If B does the work half a day, then he will do = 1/30 ÷ 2 = 1/60

Now, (A + B)'s 1 day's work = 1/20 + 1/60 = 1/15

So, A and B together will complete the work in 15 days.
৬১২.
A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is-
  1. ক
    12 days 
  2. খ
    16 days 
  3. গ
    20 days 
  4. ঘ
    24 days 
সঠিক উত্তর: ঘ
24 days 
উত্তর
সঠিক উত্তর: ঘ
24 days 
ঘ
ব্যাখ্যা
Question: A is twice as good as B and together they finish a piece of work in 16 days. The number of days taken by A alone to finish the work is-

Solution: 
let, B can do the work in 2x days 
A can do the work in x days 

ATQ,
(1/x) + (1/2x) = 1/16
⇒ 3/2x = 1/16 
⇒ x = 24 days 
৬১৩.
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
  1. ক
    34 days
  2. খ
    37 days
  3. গ
    32 days
  4. ঘ
    40 days
  5. ঙ
    38 days
সঠিক উত্তর: ঘ
40 days
উত্তর
সঠিক উত্তর: ঘ
40 days
ঘ
ব্যাখ্যা
Let 1 man's 1 day's work = x and 1 woman's 1 day's work = y
Then, 4x + 6y = 1/8 and 3x + 7y = 1/10
Solving the two equations, we get
x = 11/400, y = 1/400
∴ 1 woman's 1 day's work = 1/400
⇒ 10 women's 1 day's work = ((1/400)×10) = 1/40
Hence, 10 women will complete the work in 40 days
৬১৪.
20 buckets can fill a tank when the capacity of each bucket is 12 liters. If the capacity of each bucket is 10 liters, find the number of buckets required to fill the tank.
  1. ক
    27 buckets
  2. খ
    24 buckets
  3. গ
    34 buckets
  4. ঘ
    30 buckets
সঠিক উত্তর: খ
24 buckets
উত্তর
সঠিক উত্তর: খ
24 buckets
খ
ব্যাখ্যা
Question: 20 buckets can fill a tank when the capacity of each bucket is 12 liters. If the capacity of each bucket is 10 liters, find the number of buckets required to fill the tank.

Solution:
Capacity of each bucket = 12 liters
20 buckets can fill the tank. So, capacity of tank = 20 × 12= 240 liters

New capacity of bucket = 10 liters
So, 10 liters can be poured into the tank by 1 bucket
∴ 240 liters can be poured into the tank by (240/10) = 24 buckets
৬১৫.
Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 120 pages?
  1. ক
    ক) 6 hours
  2. খ
    খ) 9 hours
  3. গ
    গ) 10 hours
  4. ঘ
    ঘ) 12 hours
সঠিক উত্তর: খ
খ) 9 hours
উত্তর
সঠিক উত্তর: খ
খ) 9 hours
খ
ব্যাখ্যা
Number of pages typed by Ronald in 1 hour = 32/6=16/3
Number of pages typed by Elan in 1 hour = 40/5 = 8
Number of pages typed by both in 1 hour= (16/3) + 8
                                                                    = (16 + 24)/3
                                                                    =40/3

∴Time taken by both to type 120 pages
 = (120×3/40) hours
 = 9 hours
৬১৬.
Susan can type 10 pages in 5 minutes. Mary can type 5 pages in. 10 minutes. Working together, how many pages can they type in 30 minutes?
  1. ক
    15
  2. খ
    25
  3. গ
    65
  4. ঘ
    75
সঠিক উত্তর: ঘ
75
উত্তর
সঠিক উত্তর: ঘ
75
ঘ
ব্যাখ্যা
Question: Susan can type 10 pages in 5 minutes. Mary can type 5 pages in. 10 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Susan can type in 1 min = 10/5 = 2 pages 
Mary can type in 1 min = 5/10 = 1/2 page

Working together they can type in 1 min = (2 + 1/2) pages 
= 5/2 pages 

∴ They can type in 30 min = (5 × 30)/2 pages
= 75 pages
৬১৭.
A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is - 
  1. ক
    ক) 4 days
  2. খ
    খ) 6 days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 12 days
সঠিক উত্তর: ক
ক) 4 days
উত্তর
সঠিক উত্তর: ক
ক) 4 days
ক
ব্যাখ্যা
Question: A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is - 

Solution:
Ratio of rates of working of A and B = 2 : 1 
So, the ratio of time taken = 1 : 2

Since, B takes 12 days, A takes 6 days 

∴ (A + B)'s 1 day's work = (1/6) + (1/12) 
= 3/12
= 1/4 

∴ A + B can finish the work in (4/1) = 4 days
৬১৮.
X, Y, and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
  1. ক
    ক) 12
  2. খ
    খ) 16
  3. গ
    গ) 24
  4. ঘ
    ঘ) 36
সঠিক উত্তর: গ
গ) 24
উত্তর
সঠিক উত্তর: গ
গ) 24
গ
ব্যাখ্যা

(X + y)'s 1 day's work = (1/16) + (1/16)
= 2/16
= 1/8
Z's 1 day's work = (X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
= 1/6 - 1/8
= 1/24.
∴ Z alone can finish the work in 24 days.

৬১৯.
A, B and C can do a piece of work in 24, 36 and 72 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    15 days
  2. খ
    18 days
  3. গ
    10 days
  4. ঘ
    9 days
সঠিক উত্তর: খ
18 days
উত্তর
সঠিক উত্তর: খ
18 days
খ
ব্যাখ্যা

Question: A, B and C can do a piece of work in 24, 36 and 72 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? 

Solution:
A's 2 day's work = (1/24) × 2 = 1/12
∴ (A + B + C)'s 1 day's work = 1/24 + 1/36 + 1/72

= 1/24 + 1/36 + 1/72
= (3 +2 +1)/72
= 6/72
= 1/12

Work done in 3 days = 1/12+ 1/12
= 2/12
= 1/6

Now,
1/6 work is done in 3 days.
∴ Whole work will be done in (3 × 6) = 18 days

৬২০.
The cost of 21 pencils and 9 clippers is Tk. 819. The cost price of 7 pencils and 3 clippers is = ?
  1. ক
    ক) Tk. 91
  2. খ
    খ) Tk. 182
  3. গ
    গ) Tk. 273
  4. ঘ
    ঘ) Tk. 364
সঠিক উত্তর: গ
গ) Tk. 273
উত্তর
সঠিক উত্তর: গ
গ) Tk. 273
গ
ব্যাখ্যা
Cost of 21 pencils and 9 clippers = Tk. 819
That means, cost of 3(7 pencils and 3 clippers) = Tk. 819
Cost of (7 pencils and 3 clippers) = Tk.  819/3
 = Tk. 273
৬২১.
A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
  1. ক
    75
  2. খ
    82
  3. গ
    100
  4. ঘ
    110
  5. ঙ
    120
সঠিক উত্তর: ঘ
110
উত্তর
সঠিক উত্তর: ঘ
110
ঘ
ব্যাখ্যা
Question: A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Solution:
Originally let there be x men.
Less men, More days (Indirect Proportion)
Therefore, (x - 10) : x : : 100 :110
⇒ (x - 10)/x = 100/110
⇒ (x - 10) × 110 = x × 100
⇒ 11x - 110 = 10x
∴ x = 110
৬২২.
Four pipes can fill a reservoir in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 7 am, second 8 am, third at 9 am and fourth at 10 am. When will the reservoir be full?
  1. ক
    ক) 1 p.m.
  2. খ
    খ) 2 p.m.
  3. গ
    গ) 3 p.m.
  4. ঘ
    ঘ) 4 p.m.
সঠিক উত্তর: খ
খ) 2 p.m.
উত্তর
সঠিক উত্তর: খ
খ) 2 p.m.
খ
ব্যাখ্যা
Question: Four pipes can fill a reservoir in 15, 20, 30 and 60 hours respectively. The first pipe was opened at 7 am, second 8 am, third at 9 am and fourth at 10 am. When will the reservoir be full?

Solution:
Let,
the time be x hours after 7 am.
Then, the first pipe worked for x hours
Second pipe for (x - 1) hours;
Third pipe for (x - 2) hours;
Fourth pipe for (x - 3) hours.

ATQ,
(x/15) + {(x - 1)/20} + {(x - 2)/30} + {(x - 3)/60} = 1
⇒ (4x + 3x - 3 + 2x - 4 + x - 3)/60 = 1
⇒ 10x - 10 = 60
⇒ 10x = 70
∴ x = 7

So, the reservoir will be full 7 hours after 7 am = 7 + 7 = 14 = 2 p.m.
৬২৩.
A can do a piece of work in 9 days, B can do it in 12 days and C can do it in 30 days. The efficiency of D is given to be twice the efficiency of C. If A worked for 1 day, B worked for 2 days and C worked for 3 days. Find the number of days D will take to complete the remaining work alone?
  1. ক
    20/3 days
  2. খ
    25/3 days
  3. গ
    23/3 days
  4. ঘ
    28/3 days
সঠিক উত্তর: ঘ
28/3 days
উত্তর
সঠিক উত্তর: ঘ
28/3 days
ঘ
ব্যাখ্যা
Question: A can do a piece of work in 9 days, B can do it in 12 days and C can do it in 30 days. The efficiency of D is given to be twice the efficiency of C. If A worked for 1 day, B worked for 2 days and C worked for 3 days. Find the number of days D will take to complete the remaining work alone?

Solution:
A can do a piece of work in = 9 days
Work is done by A in one day = 1/9

B can do a piece of work in = 12 days
Work is done by B in one day = 1/12

C can do a piece of work in = 30 days
Work is done by C in one day = 1/30

The efficiency of D = 2 x Efficiency of C
∴ Work done by D in one day = 1/15

A worked for = 1 day
B worked for = 2 days
C worked for = 3 days

∴ Remaining work done = 1 - (1/9) - (2/12) - (3/30)
= 1- [(1/9) + (1/6) + (1/10)]
= 1 - [(10 + 15 + 9)/90]
= 1 - [34/90]
= 56/90
= 28/45

Let the time taken by D to complete the remaining work alone be x days
∴ x/15 = 28/45
∴ x = 28/3 days

D alone will take 28/3 days to finish the work.
৬২৪.
Alif can fill 60 envelopes per minute, and Tonoy can fill 40 envelopes per minute. Working together, how long will they take to fill 500 envelopes? 
  1. ক
    5 minutes
  2. খ
    4 minutes
  3. গ
    6 minutes
  4. ঘ
    8 minutes
  5. ঙ
    10 minutes
সঠিক উত্তর: ক
5 minutes
উত্তর
সঠিক উত্তর: ক
5 minutes
ক
ব্যাখ্যা

Question: Alif can fill 60 envelopes per minute, and Tonoy can fill 40 envelopes per minute. Working together, how long will they take to fill 500 envelopes?

Solution:
Given,
Alif can fill 60 envelopes in 1 minute
Tonoy can fill 40 envelopes in 1 minute

So together, they can fill in 1 minute = 60 + 40 = 100 envelopes

∴ 500 envelopes can be filled in 500 ÷ 100 = 5 minutes

৬২৫.
Hanif started a 6-mile hike with a full 10-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Hanif drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 5 miles of the hike?
  1. ক
    4/5
  2. খ
    5/6
  3. গ
    6/5
  4. ঘ
    5/4
  5. ঙ
    None of these
সঠিক উত্তর: ক
4/5
উত্তর
সঠিক উত্তর: ক
4/5
ক
ব্যাখ্যা
Question: Hanif started a 6-mile hike with a full 10-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Hanif drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 5 miles of the hike?

Solution:
No of cups leaked during the trip = 2 cups.
No of cups Harry drank = 7 cups.
No of cups harry drank during the first 5 miles = 7 - 3 = 4 cups
∴ drink/mile = 4/5
৬২৬.
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    18 days
  2. খ
    20 days
  3. গ
    15 days
  4. ঘ
    21 days
সঠিক উত্তর: গ
15 days
উত্তর
সঠিক উত্তর: গ
15 days
গ
ব্যাখ্যা

Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? 

Solution:
A's 2 day's work = (1/20) × 2 = 1/10
(A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60
= 6/60
= 1/10

Work done in 3 days = 1/10 + 1/10
= 2/10 part
= 1/ 5 part

Now,
1/5 work is done in 3 days.
∴ Whole work will be done in (3 × 5) = 15 days

৬২৭.
A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 4 days. B can do the work alone in-
  1. ক
    8 days
  2. খ
    10 days
  3. গ
    12 days
  4. ঘ
    14 days
সঠিক উত্তর: গ
12 days
উত্তর
সঠিক উত্তর: গ
12 days
গ
ব্যাখ্যা
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 4 days. B can do the work alone in-

Solution:
Suppose A, B and C take x, x/2 and x/3 days respectively to finish the work.
Then,
1/x + 2/x + 3/x = 1/4
⇒ 6/x = 1/4
⇒ x/6 = 2
∴ x = 24

So, B takes (24/2) = 12 days to finish the work.
৬২৮.
If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?
  1. ক
    7 burners
  2. খ
    5 burners
  3. গ
    8 burners
  4. ঘ
    10 burners
সঠিক উত্তর: খ
5 burners
উত্তর
সঠিক উত্তর: খ
5 burners
খ
ব্যাখ্যা
Question: If the cost of gas on burning 5 burners for 5 hours a day for 7 days is Tk. 525, then how many burners can be used for 10 days at 5 hours a day for Tk. 750?

Solution:
Given that,
5 burners 5 hours a day for 7 days is Tk. 525
Total burner-hours = (5 × 5 × 7) burner-hours
= 175 burner-hours

Cost per burner-hour =(525 ÷ 175)
= 3 Tk

∴ 750 Tk. total burner-hour = (750 ÷ 3) burner-hours
= 250 burner-hours

Let, the number of burners = x

ATQ,
x × 5 × 10 = 250
⇒ x × 50 = 250
⇒ x = 250 ÷ 50
∴ x = 5
৬২৯.
A monkey climbs a 36 m high pole. In first minute he climbs 6 m and slips down 3 m in the next minute. How much time is required by it to reach the top?
  1. ক
    20 minutes.
  2. খ
    21 minutes.
  3. গ
    22 minutes.
  4. ঘ
    25 minutes.
সঠিক উত্তর: খ
21 minutes.
উত্তর
সঠিক উত্তর: খ
21 minutes.
খ
ব্যাখ্যা
Question: A monkey climbs a 36 m high pole. In first minute he climbs 6 m and slips down 3 m in the next minute. How much time is required by it to reach the top?

Solution:
According to the question,
For 1st min, he climbs 6 m and comes down 3 m in 2nd
Effectively in 2 min, he climbs 3 m.

In 1 min, he climbs (3/2) m

So, in 20 mins he climbs = (3/2) × 20 = 30 m

So, in the 21th minute, he climbs the next 6 m.

∴ The required value is 21 minutes.
৬৩০.
A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?
  1. ক
    80
  2. খ
    85
  3. গ
    90
  4. ঘ
    95
সঠিক উত্তর: গ
90
উত্তর
সঠিক উত্তর: গ
90
গ
ব্যাখ্যা
Question: A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

Solution: 
ধরি,
১ম দিন ছিলো x টাকা 

২য় দিন = x + 10
৩য় দিন = (x + 20)
৪র্থ দিন = (x + 30)
৫ম দিন = (x + 40)
৬ষ্ঠ দিন = (x + 50) 
৭ম দিন = (x + 60) টাকা

প্রশ্নমতে,
x + (x + 10) + (x + 20) + (x + 30) = (x + 40) + (x + 50) + (x + 60)
⇒ 4x + 60 = 3x + 150
⇒ 4x - 3x = 150 - 60
∴ x = 90
৬৩১.
If 6 persons working 8 hours a day earn Tk 9600 per week, then 9 persons working 6 hours a day will earn per week?
  1. ক
    ক) 10800 Tk
  2. খ
    খ) 12000 Tk
  3. গ
    গ) 12400 Tk
  4. ঘ
    ঘ) 12800 Tk
সঠিক উত্তর: ক
ক) 10800 Tk
উত্তর
সঠিক উত্তর: ক
ক) 10800 Tk
ক
ব্যাখ্যা
Question: If 6 persons working 8 hours a day earn Tk 9600 per week, then 9 persons working 6 hours a day will earn per week?

Solution:
Earning of 6 × 8 = 48 hours is 9600 Tk
Earning of 1 hour is 9600/48 Tk
Earning of 9 × 6 = 54 hours is  (9600 × 54)/48 Tk
= 10800 Tk
৬৩২.
Hemal completes a job in 45/2 days. What part of the job will he do in 2 days?
  1. ক
    4/45
  2. খ
    1/45
  3. গ
    2/45
  4. ঘ
    8/45
  5. ঙ
    1/15
সঠিক উত্তর: ক
4/45
উত্তর
সঠিক উত্তর: ক
4/45
ক
ব্যাখ্যা
Question: Hemal completes a job in 45/2 days. What part of the job will he do in 2 days?

Solution:
We know, if a person does a job in n days, then his 1-day work = 1/n
Here,
n = 45/2
Hemal’s 1-day work = 2/45
Thus, Hemal’s 2 days work = 2 × (2/45) = 4/45
৬৩৩.
A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    15 days
  2. খ
    18 days
  3. গ
    20 days
  4. ঘ
    21 days
সঠিক উত্তর: ক
15 days
উত্তর
সঠিক উত্তর: ক
15 days
ক
ব্যাখ্যা
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Solution:
A's 2 day's work = (1/20) × 2 = 1/10
(A + B + C)'s 1 day's work = 1/20 + 1/30 + 1/60
= 6/60
= 1/10

Work done in 3 days = 1/10 + 1/10
= 2/10 part
= 1/ 5 part

Now,
1/5 work is done in 3 days.
∴ Whole work will be done in (3 × 5) = 15 days
৬৩৪.
A, B and C completed a work costing Tk. 1800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A?
  1. ক
    ক) 600
  2. খ
    খ) 750
  3. গ
    গ) 800
  4. ঘ
    ঘ) 900
সঠিক উত্তর: ক
ক) 600
উত্তর
সঠিক উত্তর: ক
ক) 600
ক
ব্যাখ্যা

Let the daily wages of A, B and C be Tk. 5x, Tk. 6x and Tk. 4x respectively.
Then, ratio of their amounts
= (5×6):(6×4):(4x9)
= 30:24:36
= 5:4:6
∴ A's amount
= Tk. (1800 × 5/15)
= Tk. 600

৬৩৫.
Given that 12 people can finish a task in 15 days, how long would it take 10 people to do the same work?
  1. ক
    10 days
  2. খ
    12 days
  3. গ
    16 days
  4. ঘ
    18 days
সঠিক উত্তর: ঘ
18 days
উত্তর
সঠিক উত্তর: ঘ
18 days
ঘ
ব্যাখ্যা
Question: Given that 12 people can finish a task in 15 days, how long would it take 10 people to do the same work?

Solution:
12 men can finish a task in 15 days
∴ 1 men can finish a task in 15 × 12 days
∴ 10 men can finish a task in (15 × 12)/10 days
= 18 days
৬৩৬.
A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 8
সঠিক উত্তর: ক
ক) 4
উত্তর
সঠিক উত্তর: ক
ক) 4
ক
ব্যাখ্যা
20 কেজি মিশ্রনে পানি আছে = 20 এর 10% 
                                            = 20 এর 10/100
                                            = 2 কেজি 

স্পিরিট আছে =20 - 2 = 18 কেজি 


ধরি,
মিশ্রনে পানি মেশাতে হবে x 

প্রশ্নমতে,
18/2 + x = 75/25
18/2 + x = 3/1 
3(2 + x)  = 18 
6 + 3x  =18
3x = 18 - 6 
3x =12
x = 4
৬৩৭.
If the workforce is tripled, how much longer will it take to finish the task?
  1. ক
    2 times
  2. খ
    1/2 times
  3. গ
    1/5 times
  4. ঘ
    1/3 times
সঠিক উত্তর: ঘ
1/3 times
উত্তর
সঠিক উত্তর: ঘ
1/3 times
ঘ
ব্যাখ্যা

Question: If the workforce is tripled, how much longer will it take to finish the task?
​
Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর তিনগুণ = ৩x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
∴ ৩x জন কাজটি করে = xn/৩x
= n/৩ সময়ে বা ১/৩ সময়ে।

৬৩৮.
Fahim's regular pay is Taka 40 per hour up to 30 hours. Overtime is 2.5 times the payment for regular time. If he was paid Taka 1680, how many hours of overtime did he work?
  1. ক
    8
  2. খ
    6
  3. গ
    5
  4. ঘ
    4
সঠিক উত্তর: গ
5
উত্তর
সঠিক উত্তর: গ
5
গ
ব্যাখ্যা
30 ঘণ্টার জন্য regular payment = (30 * 40) টাকা = 1200 টাকা
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
Over time এর প্রতিদিনের টাকার পরিমান regular payment এর 2.5 গুণ।
সুতরাং নির্ণেয় মোট সময় = 480 / (2.5 * 40) = 480/100 = 4.8 ঘণ্টা = 4 ঘণ্টা 48 মিনিট যা 5 ঘণ্টার কাছাকাছি।
৬৩৯.
75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?
  1. ক
    ক) 45
  2. খ
    খ) 55
  3. গ
    গ) 100
  4. ঘ
    ঘ) 150
সঠিক উত্তর: ক
ক) 45
উত্তর
সঠিক উত্তর: ক
ক) 45
ক
ব্যাখ্যা

Remaining work = 1 - (1/3) = 2/3
Let number of more employees needed be E
Thus (75+E) employees complete 2/3 works in 50 hours.
∴ 75 employes × 40 hours × (2/3) = (75 + E) × 50 hours × (1/3)
∴ E = 45 = these many more employees are needed.

৬৪০.
A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
  1. ক
    ক) 75
  2. খ
    খ) 82
  3. গ
    গ) 100
  4. ঘ
    ঘ) 110
  5. ঙ
    ঙ) 120
সঠিক উত্তর: ঘ
ঘ) 110
উত্তর
সঠিক উত্তর: ঘ
ঘ) 110
ঘ
ব্যাখ্যা

Originally let there be x men.

Less men, More days (Indirect Proportion)

Therefore, (x - 10) : x :: 100 :110

=> (x - 10) × 110 = x × 100
=> x = 110

৬৪১.
Arif and Mahir can clean the garage together in 6 hours. If it takes Arif 8 hours working alone, how long will it take Mahir working alone?
  1. ক
    ক) 12 hours
  2. খ
    খ) 16 hours
  3. গ
    গ) 18 hours
  4. ঘ
    ঘ) 24 hours
সঠিক উত্তর: ঘ
ঘ) 24 hours
উত্তর
সঠিক উত্তর: ঘ
ঘ) 24 hours
ঘ
ব্যাখ্যা

দুই জন একত্রে ১ ঘণ্টায় কাজ করতে পারে ১/৬ অংশ।
আরিফ ১ ঘণ্টায় কাজ করতে পারে ১/৮ অংশ।
মাহির একা ১ ঘণ্টায় করতে পারে (১/৬ - ১/৮) = (৮-৬)/৪৮ = ১/২৪ অংশ।
∴ মাহির একা পুরো কাজটি করতে পারবে  = ২৪ ঘণ্টায়

৬৪২.
A complete 1/8 of a work in one day. B with double efficiency can do the full work in -
  1. ক
    ক) 6 days
  2. খ
    খ) 7 days
  3. গ
    গ) 4 days
  4. ঘ
    ঘ) 2 days
সঠিক উত্তর: গ
গ) 4 days
উত্তর
সঠিক উত্তর: গ
গ) 4 days
গ
ব্যাখ্যা
Question: A complete 1/8 of a work in one day. B with double efficiency can do the full work in - 

Solution:
যেহেতু B এর দক্ষতা A এর দ্বিগুণ তাই B একদিনে A এর চেয়ে দ্বিগুণ কাজ করবে।
∴ B একদিনে করবে = ২ × ১/৮ = ১/৪ অংশ

সম্পূর্ণ কাজ করবে = ৪ দিনে
৬৪৩.
A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work-
  1. ক
    3 days
  2. খ
    4 days
  3. গ
    5 days
  4. ঘ
    6 days
সঠিক উত্তর: খ
4 days
উত্তর
সঠিক উত্তর: খ
4 days
খ
ব্যাখ্যা
Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days  

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days
৬৪৪.
A pump removes water at a rate of 6 gallons per minute. How many hours will it take to remove 1800 gallons?
  1. ক
    3 hours
  2. খ
    4 hours
  3. গ
    5 hours
  4. ঘ
    6 hours
সঠিক উত্তর: গ
5 hours
উত্তর
সঠিক উত্তর: গ
5 hours
গ
ব্যাখ্যা
Question: A pump removes water at a rate of 6 gallons per minute. How many hours will it take to remove 1800 gallons?

Solution:
Required time = 1800/6 mins 
= 300/60 hours
= 5 hours
৬৪৫.
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
  1. ক
    ক) 40 days
  2. খ
    খ) 36 days
  3. গ
    গ) 32 days
  4. ঘ
    ঘ) 34 days
সঠিক উত্তর: ক
ক) 40 days
উত্তর
সঠিক উত্তর: ক
ক) 40 days
ক
ব্যাখ্যা
Question: 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Solution: 
let, work done by one man in one day = x
work done by one woman in one day = y 

so,
in one day 4 men and 6 women can do = 1/8
∴ 4x + 6y = 1/8 . . . . (i)

and 3x + 7y = 1/10 . . . (ii)

multiplying (i) by 3 and (ii) by 4 and then subtracting we get,
12x + 18y - 12x - 28y = 3/8 - 4/10
- 10y = - 1/40
10y = 1/40

hence, 10 women can finish the work in 40 days
৬৪৬.
Ruman was told to work 8 hours for the company everyday with 8 days leave for the month of January. But he spent 3 days extra as leave. How much time he has to work extra to equalize the working hour for the month January?
  1. ক
    ক) 1.2 hours
  2. খ
    খ) 1.3 hours
  3. গ
    গ) 1.4 hours
  4. ঘ
    ঘ) 1.5 hours
সঠিক উত্তর: ক
ক) 1.2 hours
উত্তর
সঠিক উত্তর: ক
ক) 1.2 hours
ক
ব্যাখ্যা
Question: Ruman was told to work 8 hours for the company everyday with 8 days leave for the month of January. But he spent 3 days extra as leave. How much time he has to work extra to equalize the working hour for the month January?

Solution:
৮ দিনের বন্ধের পর জানুয়ারি মাসে বাকি থাকে (৩১ - ৮) বা, ২৩ দিন।
২৩ দিনে কাজ করার কথা (২৩ × ৮) ঘণ্টা বা, ১৮৪ ঘন্টা

৩ দিন অতিরিক্ত কাজ না করায় বাকি দিন রইলো = ২৩ - ৩ = ২০ দিন।

তাহলে প্রতিদিন কাজ করতে হবে = ১৮৪/২০ = ৯.২ ঘণ্টা।

প্রতিদিন অতিরিক্ত  কাজ করতে হবে = (৯.২ - ৮) = ১.২ ঘণ্টা
৬৪৭.
P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if they work together. How much time will Q take to do the work alone?
  1. ক
    ক) 4 days
  2. খ
    খ) 5 days
  3. গ
    গ) 6 days
  4. ঘ
    ঘ) 7 days
সঠিক উত্তর: গ
গ) 6 days
উত্তর
সঠিক উত্তর: গ
গ) 6 days
গ
ব্যাখ্যা

Let,
The amount of work P does in 1 day = x
Amount of work Q does in 1 day = 2x
Amount of work R does in 1 day = 3x

Amount of work P, Q,R together do in 1 day = x + 2x + 3x = 6x
they can together complete the work in 1 day = (1/6x) days

Given,
1/6x = 2
⇒ 12x = 1
⇒ x = 1/12

Therefore, amount of work Q does in 1 day = 2 × (1/12) = 1/6
That is, Q needs 6 days to complete the work.

৬৪৮.
Some persons can do a piece of work in 24 days. Two times the number of such persons will do half of that work in -
  1. ক
    ক) 6 days
  2. খ
    খ) 3 days
  3. গ
    গ) 12 days
  4. ঘ
    ঘ) 8 days
সঠিক উত্তর: ক
ক) 6 days
উত্তর
সঠিক উত্তর: ক
ক) 6 days
ক
ব্যাখ্যা
Question: Some persons can do a piece of work in 24 days. Two times the number of such persons will do half of that work in -

Solution:
Let the initial workers be x
So, workers for 2nd time = 2x

x persons can complete 1 part in 24 days
1 person can complete 1 part in 24x days
2x persons can complete 1/2 part in 24x/(2x × 2) days
= 6 days
৬৪৯.
A canteen requires 651 liters of water for a week. Totally, how many liters will it require for the months of December, January, February?
  1. ক
    ক) 8370 liters
  2. খ
    খ) 8470 liters
  3. গ
    গ) 8650 liters
  4. ঘ
    ঘ) 9857 liters
সঠিক উত্তর: ক
ক) 8370 liters
উত্তর
সঠিক উত্তর: ক
ক) 8370 liters
ক
ব্যাখ্যা
Question: A canteen requires 651 liters of water for a week. Totally, how many liters will it require for the months of December, January, February?

Solution: 

একদিনে পানি লাগে = 651/7 = 93 লিটার

ডিসেম্বর, জানুয়ারি, ফেব্রুয়ারি তে মোট দিন = (31 + 31 + 28) = 90 দিন।

মোট পানি লাগবে = (90 × 93) = 8370 লিটার
৬৫০.
If 2 kg of almonds cost as much as 8 kg of walnuts, and the cost of 5 kg of almonds and 16 kg of walnuts is Tk. 1080, what is the cost of almonds per kg?
  1. ক
    Tk. 160
  2. খ
    Tk. 120
  3. গ
    Tk. 150
  4. ঘ
    None of these.
সঠিক উত্তর: খ
Tk. 120
উত্তর
সঠিক উত্তর: খ
Tk. 120
খ
ব্যাখ্যা
Question: If 2 kg of almonds cost as much as 8 kg of walnuts, and the cost of 5 kg of almonds and 16 kg of walnuts is Tk. 1080, what is the cost of almonds per kg?

Solution:
Let the cost of almond per kg be Tk. x, and the cost of walnuts per kg be Tk. y.
Now, ATQ,
2x = 8y
or, x = 4y

Now,
5x + 16y = 1080
Or, 5x + 4x = 1080
Or, x = 120

Therefore, the cost price of almond per kg = Tk. 120
৬৫১.
A does half as much as work as B in 1/6 of the time taken by B. Together they can complete the work in 10 days. B alone can complete the work in how many days?
  1. ক
    20 days
  2. খ
    30 days
  3. গ
    40 days
  4. ঘ
    50 days
সঠিক উত্তর: গ
40 days
উত্তর
সঠিক উত্তর: গ
40 days
গ
ব্যাখ্যা

Let B does 1 work in x days
Then, A does [1/2] work in x/6 days
To do 1 unit work, A will take x/3 days

That means the time ratio of A: B = x: x/3
Or time ratio = 1: 1/3
Or time ratio = 3: 1

As we know that the efficiency ratio is inversely proportional to the time ratio

i.e., Efficiency ratio of A: B = 1: 3

ATQ,

(A + B) = 10 days
Total work = days × efficiency of (A + B)
Or, total work = 10 × 4 = 40 units
i.e., B can finish the work in = total work/ efficiency of B

So, B can finish the work in 40/1 = 40 days.

৬৫২.
The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?
  1. ক
    ক) 20%
  2. খ
    খ) 25%
  3. গ
    গ) 50%
  4. ঘ
    ঘ) 37.5%
সঠিক উত্তর: ক
ক) 20%
উত্তর
সঠিক উত্তর: ক
ক) 20%
ক
ব্যাখ্যা
ধরি
বইয়ের দাম = ১০০ টাকা 
কলমের দাম = ১০০ + ২৫ টাকা 
                      = ১২৫ টাকা 

কলমদানির দাম = ১২৫ + ২৫ = ১৫০ টাকা 


কলম থেকে কলমদানির দাম  = (১৫০ - ১২৫) টাকা 
                                              = ২৫ টাকা 

কলম থেকে কলম দানি শতকরা বেশি =(২৫ × ১০০)/১২৫
                                                         = ২০ টাকা
৬৫৩.
A map has a scale of 1 cm to 3 km, what length on actual ground does a 3 cm length on the map represent?
  1. ক
    5 km
  2. খ
    9 km
  3. গ
    12 km
  4. ঘ
    None of these
সঠিক উত্তর: খ
9 km
উত্তর
সঠিক উত্তর: খ
9 km
খ
ব্যাখ্যা
Question: A map has a scale of 1 cm to 3 km, what length on actual ground does a 3 cm length on the map represent?

Solution: 
Given that,
1 cm represents 3 km 
∴ 3 cm represent (3 × 3) km 
= 9 km
৬৫৪.
If 20 boys or 10 men can make 20 cricket bats in 10 days, then how many cricket bats will be made by 4 boys and 8 men in 20 days?
  1. ক
    20 cricket bats
  2. খ
    30 cricket bats
  3. গ
    40 cricket bats
  4. ঘ
    60 cricket bats
সঠিক উত্তর: গ
40 cricket bats
উত্তর
সঠিক উত্তর: গ
40 cricket bats
গ
ব্যাখ্যা
Question: If 20 boys or 10 men can make 20 cricket bats in 10 days, then how many cricket bats will be made by 4 boys and 8 men in 20 days?

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

If 20 boys can make 20 cricket bats in 10 days,
8 men and 4 boys or, (16 + 4) = 20 boys can make in 20 days = (20 × 2) cricket bats
= 40 cricket bats
৬৫৫.
A man can do a work in 20 days and a woman in 15 days. If they work on it together for 5 days, then the fraction of the work that is left-
  1. ক
    8/15
  2. খ
    1/12
  3. গ
    5/12
  4. ঘ
    None of these
সঠিক উত্তর: গ
5/12
উত্তর
সঠিক উত্তর: গ
5/12
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 5 days, then the fraction of the work that is left-

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)  = (3 + 4)/60 = 7/60
∴ (Man + woman)'s 5 day's work = (7/60) × 5 = 7/12

Thus, Remaining work = 1 - (7/12) = (12 - 7)/12 = 5/12

∴ The fraction of the work that is left = 5/12
৬৫৬.
A sum of money is sufficient to pay A's wages for 21 days or B's wages for 28 days. The same money is sufficient to pay the wages of both for?
  1. ক
    24 days
  2. খ
    18 days
  3. গ
    12 days
  4. ঘ
    8 days
সঠিক উত্তর: গ
12 days
উত্তর
সঠিক উত্তর: গ
12 days
গ
ব্যাখ্যা
Question: A sum of money is sufficient to pay A's wages for 21 days or B's wages for 28 days. The same money is sufficient to pay the wages of both for?

Solution:
Let
total money be Tk. x
A's 1 day's wages = Tk. x/21
B's 1 day's wages = Tk. x/28

∴ (A + B)'s 1 day's wages = Tk. (x/21 + x/28)
= Tk. (4x + 3x)/84
= Tk. 7x/84
= Tk. x/12

∴ Money is sufficient to pay the wages of both for 12 days.
৬৫৭.
A man completes (1/3) of a job in 13 days. At this rate, how many more days will it take him to finish the job?
  1. ক
    20 days
  2. খ
    16 days
  3. গ
    36 days
  4. ঘ
    26 days
সঠিক উত্তর: ঘ
26 days
উত্তর
সঠিক উত্তর: ঘ
26 days
ঘ
ব্যাখ্যা

Question: A man completes (1/3) of a job in 13 days. At this rate, how many more days will it take him to finish the job?

Solution:
 

Work done = 1/3

Balance work =(1−1/3) = 2/3

Less work, Less days ( Direct proportion)
Let the required number of days be x
Then,
⇔ (1/3) : (2/3) : : 13 : X
⇔ (1/3)/(2/3) = 13/X
⇔ 1/2 = 13/X
⇔ X = 13 × 2 = 26 days

৬৫৮.
Sifat and Rifat can complete a task individually in 18 and 27 days, respectively. After working together for 9 days, Rifat leaves. How many days does Sifat need to complete the rest?
  1. ক
    1 days
  2. খ
    2 days
  3. গ
    3 days
  4. ঘ
    6 days
সঠিক উত্তর: গ
3 days
উত্তর
সঠিক উত্তর: গ
3 days
গ
ব্যাখ্যা
Question: Sifat and Rifat can complete a task individually in 18 and 27 days, respectively. After working together for 9 days, Rifat leaves. How many days does Sifat need to complete the rest?

Solution:

৬৫৯.
If 12 men or 18 boys can make 90 chairs in 9 days, then how many chairs will be made by 6 men and 9 boys in 10 days?
  1. ক
    50 chairs
  2. খ
    70 chairs
  3. গ
    80 chairs
  4. ঘ
    100 chairs
সঠিক উত্তর: ঘ
100 chairs
উত্তর
সঠিক উত্তর: ঘ
100 chairs
ঘ
ব্যাখ্যা
Question: If 12 men or 18 boys can make 90 chairs in 9 days, then how many chairs will be made by 6 men and 9 boys in 10 days?

Solution:
Here, 
12 men = 18 boys
∴ 6 men = (18 ÷ 2) boys
= 9 boys

∴ 6 men and 9 boys = (9 + 9) = 18 boys

Now,
18 boys can make 90 chairs in 9 days
In 1 day, 18 boys can make (90/9) =10 chairs
∴ In 10 day, 18 boys can make = (10 × 10) chairs
= 100 chairs
৬৬০.
Joy can knit a pair of socks in 3 days. Belal can knit the same pair of socks in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks?
  1. ক
    9/2 days
  2. খ
    9/4 days
  3. গ
    9/8 days
  4. ঘ
    None of these
সঠিক উত্তর: ক
9/2 days
উত্তর
সঠিক উত্তর: ক
9/2 days
ক
ব্যাখ্যা
Question: Joy can knit a pair of socks in 3 days. Belal can knit the same pair of socks in 9 days. If they are knitting together, then in how many days will they knit two pairs of socks?

Solution: 
They knit in one day = (1/3) + (1/9)
= 4/9 days

They knit a pair of socks in 9/4 days
they knit two pairs of socks in (9 × 2)/4 days 
= 9/2 days
৬৬১.
A can do a piece of work in 8 days working 12 hours per day. If B is two-thirds as efficient as A, then in how many days B alone do the same piece of work, working 4 hours per day?
  1. ক
    ক) 28 days
  2. খ
    খ) 31 days
  3. গ
    গ) 36 days
  4. ঘ
    ঘ) 43 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 8 days working 12 hours per day. If B is two-thirds as efficient as A, then in how many days B alone do the same piece of work, working 4 hours per day?

Solution:
Time taken by A alone to do the work = 8×12 = 96 hrs.
 Since B is 2/3 efficient as A, so time taken by B is 3/2 times of A = ( 96×3/2 ) hrs = 144 hrs.
∴ Required days = ( 144/4 ) = 36 days.
৬৬২.
If 4 men or 6 women can complete a work in 20 days, how many days would it take 6 men and 11 women to complete twice the work?
  1. ক
    12 days
  2. খ
    16 days
  3. গ
    20 days
  4. ঘ
    24 days
সঠিক উত্তর: ক
12 days
উত্তর
সঠিক উত্তর: ক
12 days
ক
ব্যাখ্যা

Question: If 4 men or 6 women can complete a work in 20 days, how many days would it take 6 men and 11 women to complete twice the work?

Solution:
এখানে,
4 men = 6 women
∴ 1 man = 6/4 = 3/2 women
∴ 6 men = 6 × 3/2 = 9 women
∴ 6 men and 11 women together = 9 + 11 = 20 women

6 women কাজটি সম্পন্ন করে = 20 দিনে
∴ 1 woman কাজটি সম্পন্ন করে = 20 × 6 = 120 দিনে
∴ 20 women কাজটি সম্পন্ন করে = 120/20 = 6 দিনে

সুতরাং, দ্বিগুণ (twice) কাজ সম্পন্ন করতে সময় লাগবে = 6 × 2 = 12 দিন

৬৬৩.
One machine can produce one mobile in one minute. How much time will 100 machines take to produce 100 mobiles?
  1. ক
    ক) 100 minutes
  2. খ
    খ) 1 hour
  3. গ
    গ) 1 minute
  4. ঘ
    ঘ) 20 minutes
সঠিক উত্তর: গ
গ) 1 minute
উত্তর
সঠিক উত্তর: গ
গ) 1 minute
গ
ব্যাখ্যা
Question: One machine can produce one mobile in one minute. How much time will 100 machines take to produce 100 mobiles?

Solution:
১ টি মেশিন ১ টি মোবাইল তৈরি করে ১ মিনিটে
১ টি মেশিন ১০০ টি মোবাইল তৈরি করে (১ × ১০০) মিনিটে
১০০ টি মেশিন ১০০ টি মোবাইল তৈরি করে (১ × ১০০)/১০০ মিনিটে
= ১ মিনিটে
৬৬৪.
A can do a piece of work in 30 days. When he had worked for 10 days, B joined him. If the complete work was finished in 24 days, B can alone finish that work in - 
  1. ক
    50 days
  2. খ
    60 days
  3. গ
    70 days
  4. ঘ
    30 days
সঠিক উত্তর: গ
70 days
উত্তর
সঠিক উত্তর: গ
70 days
গ
ব্যাখ্যা

Question: A can do a piece of work in 30 days. When he had worked for 10 days, B joined him. If the complete work was finished in 24 days, B can alone finish that work in -

 
Solution:

A's 1 day's work = 1/30 part
A's 24 day's work = 24/30 part = 4/5 part

∴ Remaining work = 1 - 4/5 = 1/5 part

This 1/5 part of work was done by B in = (24 - 10) = 14 days

∴ 1 part of work done by B in = 14 × 5 = 70 days

৬৬৫.
A project scheduled to be carried out over a single fiscal year has a budget of Tk. 12,600, divided into12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was Tk. 4,580. By how much was the project over its budget?
  1. ক
    Tk. 380
  2. খ
    Tk. 540
  3. গ
    Tk. 1,050
  4. ঘ
    Tk. 1,380
  5. ঙ
    Tk. 1,430
সঠিক উত্তর: ক
Tk. 380
উত্তর
সঠিক উত্তর: ক
Tk. 380
ক
ব্যাখ্যা
Question: A project scheduled to be carried out over a single fiscal year has a budget of Tk. 12,600, divided into12 equal monthly allocations. At the end of the fourth month of that fiscal year, the total amount actually spent on the project was Tk. 4,580. By how much was the project over its budget?

Solution:
Each month's budget = 12600/12 = 1050
Budget for 4 months = 4 × 1050 = 4200
Actual amount spent = 4580
Amount spent over the budget = 4580 - 4200 = 380
৬৬৬.
If 3 men or 6 women can plough a field in 42 days, how long will 8 men and 5 women take to plough it?
  1. ক
    14 days
  2. খ
    13 days
  3. গ
    12 days
  4. ঘ
    10 days
সঠিক উত্তর: গ
12 days
উত্তর
সঠিক উত্তর: গ
12 days
গ
ব্যাখ্যা

Question: If 3 men or 6 women can plough a field in 42 days, how long will 8 men and 5 women take to plough it?

Solution: 
3 men or 6 women can plough the field in 42 days

3 men = 6 women
1 men = (6/3) women
8 men = {(6/3) × 8} = 16 women

∴ 8 men and 5 women = 16 + 5 = 21 women

6 women can plough field in 42 days
1 women can plough field in (42 × 6) days
∴ 21 women can plough field in (42 × 6)/21 = 12 days

৬৬৭.
5 mat-weavers can weave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?
  1. ক
    ক) 5 mats
  2. খ
    খ) 10 mats
  3. গ
    গ) 20 mats
  4. ঘ
    ঘ) 15 mats
সঠিক উত্তর: গ
গ) 20 mats
উত্তর
সঠিক উত্তর: গ
গ) 20 mats
গ
ব্যাখ্যা
Question: 5 mat-weavers can weave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-weavers in 10 days?

Solution:
5 mat-weavers in 5 days can weave 5 mats
1 mat-weaver in 1 day can weave 5/(5 × 5) mats
10 mat-weavers in 10 days can weave (5 × 10 × 10)/(5 × 5) mats
= 20 mats
৬৬৮.
If Shorna had twice the amount of money that she has, she would have exactly the amount necessary to buy 3 hamburgers at Tk. 96 apiece and 2 milk shakes at Tk. 128 apiece. How much money does Shorna have?
  1. ক
    Tk. 160
  2. খ
    Tk. 224
  3. গ
    Tk. 272
  4. ঘ
    Tk. 336
  5. ঙ
    Tk. 544
সঠিক উত্তর: গ
Tk. 272
উত্তর
সঠিক উত্তর: গ
Tk. 272
গ
ব্যাখ্যা
Question: If Shorna had twice the amount of money that she has, she would have exactly the amount necessary to buy 3 hamburgers at Tk. 96 apiece and 2 milk shakes at Tk. 128 apiece. How much money does Shorna have?

Solution:
Price of 3 hamburgers and 2 milk shakes = 96 × 3 + 128 × 2 = 288 + 256 = Tk. 544

But she only has half of that money, which is 544/2 = Tk. 272
৬৬৯.
If 2 < x < 5 and 3 < y < 5, which of the following best describes x - y?
  1. ক
    - 3 < x - y < 2
  2. খ
    - 3 < x - y < 5
  3. গ
    0 < x - y < 2
  4. ঘ
    3 < x - y < 5
  5. ঙ
    2 < x - y < 5
সঠিক উত্তর: ক
- 3 < x - y < 2
উত্তর
সঠিক উত্তর: ক
- 3 < x - y < 2
ক
ব্যাখ্যা

Question: If 2 < x < 5 and 3 < y < 5, which of the following best describes x - y?

Solution:
দেয়া আছে,
2 < x < 5
3 < y < 5

এখন, আমরা x - y এর সীমা বের করতে চাই। এর জন্য, y এর অসমতাকে - y এর অসমতায় রূপান্তর করতে হবে।
3 < y < 5
⇒ - 3 > - y > - 5 [- 1 দ্বারা গুণ করে]
⇒ - 5 < - y < - 3 

এইবার x এবং - y এর অসমতা দুটি যোগ করি,
⇒ (2 < x < 5) + (- 5 < - y < - 3)
⇒ −3 < x - y < 2

৬৭০.
12 examiners (men) work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would work how many hours per day to check 36000 answer sheets in 36 days?
  1. ক
    6 hours
  2. খ
    8 hours
  3. গ
    12 hours
  4. ঘ
    16 hours
  5. ঙ
    None of these
সঠিক উত্তর: ক
6 hours
উত্তর
সঠিক উত্তর: ক
6 hours
ক
ব্যাখ্যা
Question: 12 examiners (men) work 16 hours a day to check 24000 answer sheets in 18 days. Now, 24 examiners would work how many hours per day to check 36000 answer sheets in 36 days?

Solution:
১২ জন ১৮ দিনে ২৪০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে ১৬ ঘণ্টা
১২ জন ১৮ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে ১৬/২৪০০০ ঘণ্টা
১২ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮)/২৪০০০ ঘণ্টা
১ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২)/২৪০০০  ঘণ্টা
২৪ জন ১ দিনে ১টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২)/(২৪০০০ × ২৪) ঘণ্টা
২৪ জন ১ দিনে ৩৬০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২ × ৩৬০০০)/(২৪০০০ × ২৪) ঘণ্টা
২৪ জন ৩৬ দিনে ৩৬০০০টি উত্তর পত্র যাচাই করতে দৈনিক কাজ করে (১৬ × ১৮ × ১২ × ৩৬০০০)/(২৪০০০ × ২৪ × ৩৬) ঘণ্টা
= ৬ ঘণ্টা
৬৭১.
A certain business printer can print 40 characters per second, which is 4 times as fast as an average printer. If an average printer can print 5 times as fast as an electric typewriter, how many characters per minute can an electric typewriter print?
  1. ক
    2
  2. খ
    32
  3. গ
    50
  4. ঘ
    120
সঠিক উত্তর: ঘ
120
উত্তর
সঠিক উত্তর: ঘ
120
ঘ
ব্যাখ্যা
Question: A certain business printer can print 40 characters per second, which is 4 times as fast as an average printer. If an average printer can print 5 times as fast as an electric typewriter, how many characters per minute can an electric typewriter print?

Solution:
Rate at which business printer can print = 40 char per second
Rate at which an average printer can print = (40/4) char per second = 10 char per second

Average printer's rate = 5 × Electric typewriter's rate
⇒ Electric typewriter's rate = 10/5 = 2 char per second
⇒ 2 × 60 char per min = 120 char per min
৬৭২.
If the cost of x metres of wire is d Taka, then what is the cost of y metres of wire at the same rate?
  1. ক
    ক) Tk. (xy)/d
  2. খ
    খ) Tk. xd
  3. গ
    গ) Tk. yd
  4. ঘ
    ঘ) Tk. (yd)/x
সঠিক উত্তর: ঘ
ঘ) Tk. (yd)/x
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. (yd)/x
ঘ
ব্যাখ্যা
প্রশ্ন: If the cost of x metres of wire is d Taka, then what is the cost of y metres of wire at the same rate?

সমাধান: 
x মিটারের দাম d টাকা 
∴ 1 মিটারের দাম d/x টাকা
∴ y মিটারের দাম (yd)/x টাকা
৬৭৩.
If 2 tables and 3 chairs cost Tk. 4800 and 3 tables and 2 chairs cost Tk. 5700, then how much does a table cost?
  1. ক
    1000 Tk
  2. খ
    1200 Tk
  3. গ
    1500 Tk
  4. ঘ
    1300 Tk
সঠিক উত্তর: গ
1500 Tk
উত্তর
সঠিক উত্তর: গ
1500 Tk
গ
ব্যাখ্যা
Question: If 2 tables and 3 chairs cost Tk. 4800 and 3 tables and 2 chairs cost Tk. 5700, then how much does a table cost?

Solution:
Let
The cost of a table and that of a chair be Tk. x and Tk. y respectively.

Then,
2x + 3y = 4800................(i)
and
3x + 2y = 5700................(ii)

(ii)× 3 - (i) × 2 ⇒
9x + 6y - 4x - 6y = 17100 - 9600
5x = 7500
x = 1500

The cost of a table Tk. 1500
৬৭৪.
If 12 men or 18 boys can make 360 baskets in 15 days, then how many baskets will be made by 10 men and 15 boys in 15 days?
  1. ক
    100 baskets
  2. খ
    600 baskets
  3. গ
    500 baskets
  4. ঘ
    400 baskets
সঠিক উত্তর: খ
600 baskets
উত্তর
সঠিক উত্তর: খ
600 baskets
খ
ব্যাখ্যা

Question: If 12 men or 18 boys can make 360 baskets in 15 days, then how many baskets will be made by 10 men and 15 boys in 15 days?

Solution:
Here,
12 men = 18 boys
∴ 1 man = 18/12 boys
= 3/2 boys

∴ 10 men = (3/2) × 10 = 15 boys
∴ 10 men and 15 boys = 15 boys + 15 boys
= 30 boys

18 boys can make 360 baskets in 15 days
∴ 1 boy can make in 15 days = 360/18 = 20 baskets
∴ 30 boys can make in 15 days = 20 × 30 = 600 baskets

∴ 10 men and 15 boys can make 600 baskets.

৬৭৫.
A certain machine produces 1,000 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 7 days?
  1. ক
    ক) 7,000
  2. খ
    খ) 24,000
  3. গ
    গ) 40,000
  4. ঘ
    ঘ) 168,000
সঠিক উত্তর: ঘ
ঘ) 168,000
উত্তর
সঠিক উত্তর: ঘ
ঘ) 168,000
ঘ
ব্যাখ্যা
7 days = 7 × 24 hours = 168 hours
In 1 hour, the machine produces 1,000 units
In 168 hours, the machine produces 1,000 × 168  units = 168000 units
৬৭৬.
A and B together can do a piece of work in 40 days. A having worked for 20 days, B finishes the remaining work alone in 60 days. In How many days shall B finish the whole work alone?
  1. ক
    ক) 60 days
  2. খ
    খ) 70 days
  3. গ
    গ) 80 days
  4. ঘ
    ঘ) 90 days
সঠিক উত্তর: গ
গ) 80 days
উত্তর
সঠিক উত্তর: গ
গ) 80 days
গ
ব্যাখ্যা

Let A's 1 day's work = x and B's 1 day's work = y
Then, x+y = 1/40 and 20x+60y = 1
Solving these two equations, we get, x = 1/80 and y = 1/80
Therefore B's 1 day work = 1/80
Hence, B alone shall finish the whole work in 80 days

৬৭৭.
Himu can complete a piece of work in 30 days and Nazmul in 40 days. Find the remaining work left to complete, if they work together for 8 days -
  1. ক
    2/5
  2. খ
    1/12
  3. গ
    8/15
  4. ঘ
    4/19
সঠিক উত্তর: গ
8/15
উত্তর
সঠিক উত্তর: গ
8/15
গ
ব্যাখ্যা

Himu's 1 day work = 1/30
Nazmul's 1 day work = 1/40
Then, (Himu + Nazmul)'s 1 day work = 1/30 + 1/40
= 7/120
And (Himu + Nazmul)'s 8 day's work = 8 x (7/120)
= 7/15
Therefore, Remaining work = (1 - 7/15)
= 8/15.

৬৭৮.
Provisions for a camp were planned for 120 men or 200 children. After 150 children have eaten, how many men can still be served?
  1. ক
    30
  2. খ
    20
  3. গ
    40
  4. ঘ
    35
সঠিক উত্তর: ক
30
উত্তর
সঠিক উত্তর: ক
30
ক
ব্যাখ্যা
Question: Provisions for a camp were planned for 120 men or 200 children. After 150 children have eaten, how many men can still be served?

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
৬৭৯.
A computer programmer needs to print 148 documents. The documents have an average (arithmetic mean) length of 10 pages and the printer takes 15 seconds to print each page. Approximately how many hours will it take to print all the documents if they are printed without interruptions?
  1. ক
    0.5 hr
  2. খ
    2 hr
  3. গ
    2.5 hr
  4. ঘ
    6 hr
সঠিক উত্তর: ঘ
6 hr
উত্তর
সঠিক উত্তর: ঘ
6 hr
ঘ
ব্যাখ্যা
Question: A computer programmer needs to print 148 documents. The documents have an average (arithmetic mean) length of 10 pages and the printer takes 15 seconds to print each page. Approximately how many hours will it take to print all the documents if they are printed without interruptions?

Solution:
Number of Documents = 148.
Avg. Number of pages per document = 10.
Total Pages = 148 × 10 = 1480.

Speed of Printer = 15 Seconds Per Page.

1 Page = 15 Seconds.
1480 Pages = 15 × 1480 = 22200 Seconds.
Value in Hours = 22200/(60 × 60) = 6.16 hours ≈ 6 Hours.
৬৮০.
A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 
  1. ক
    3 days
  2. খ
    4 days
  3. গ
    5 days
  4. ঘ
    6 days
সঠিক উত্তর: খ
4 days
উত্তর
সঠিক উত্তর: খ
4 days
খ
ব্যাখ্যা
Question: A works twice as fast as B. If B can complete a work in 12 days immediately, the number of days in which A and B can together finish the work- 

Solution:
B can complete a work in 12 days
So, A can complete the work in 6 days  

(A + B)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (A + B) can complete the work in 4 days
৬৮১.
If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?
  1. ক
    1 days 
  2. খ
    3 days 
  3. গ
    6 days 
  4. ঘ
    9 days 
সঠিক উত্তর: খ
3 days 
উত্তর
সঠিক উত্তর: খ
3 days 
খ
ব্যাখ্যা
Question:  If 3 spiders make 3 webs in 3 days, then 1 spider will make 1 web in how many days?

Solution: 
3 spiders can make 3 webs in 3 days,
3 spiders can make 1 webs in 3/3 days,
1 spiders can make 1 webs in (3 × 3)/3 = 3 days
৬৮২.
An air conditioner can cool the hall in 40 miutes while another takes 60 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room?
  1. ক
    24 minutes
  2. খ
    26 minutes
  3. গ
    28 minutes
  4. ঘ
    None of these
সঠিক উত্তর: ক
24 minutes
উত্তর
সঠিক উত্তর: ক
24 minutes
ক
ব্যাখ্যা
Question: An air conditioner can cool the hall in 40 miutes while another takes 60 minutes to cool under similar conditions. If both air conditioners are switched on at same instance then how long will it take to cool the room?

Solution: 
৪০ মিনিটে ঠান্ডা হয় সম্পূর্ণ অংশ 
১ মিনিটে পূর্ণ হয় ১/৪০ অংশ 


৬০ মিনিটে পূর্ণ হয় সম্পূর্ণ অংশ 
১ মিনিটে পূর্ণ হয় ১/৬০ অংশ  


দুটি মিলে পূর্ণ হয় ১/৪০ + ১/৬০ 
= ৩ + ২ / ১২০
= ৫/১২০ মিনিট 
= ১/২৪ মিনিট 

সম্পূর্ণ অংশ ঠান্ডা হতে সময় লাগে ২৪ মিনিট। 
৬৮৩.
If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?
  1. ক
    200 hectares
  2. খ
    220 hectares
  3. গ
    250 hectares
  4. ঘ
    280 hectares
সঠিক উত্তর: গ
250 hectares
উত্তর
সঠিক উত্তর: গ
250 hectares
গ
ব্যাখ্যা
Question: If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?

Solution: 
8 men can reap  in 12 days 40 hectares
1 men can reap  in 1 days  40/(12 × 8) hectares
30 men reap in 20 days = (40 × 600)/96
= 250 hectares
৬৮৪.
If the Price of 6 toys is Tk. 264.37. What will be the approximate price of 5 toys?
  1. ক
    ক) Tk. 120
  2. খ
    খ) Tk. 100
  3. গ
    গ) Tk..200
  4. ঘ
    ঘ) Tk. 220
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: ঘ
ঘ) Tk. 220
উত্তর
সঠিক উত্তর: ঘ
ঘ) Tk. 220
ঘ
ব্যাখ্যা

Let the required Price be Tk. X .
Then, Lest toys , Less cost (Direct Proportion)
Therefore 6 : 5 :: 264.37 : x
=> 6 × x = 5 × 264.37
=> x = 220.308
Therefore, Approximate price of 5 toys = Tk. 220

৬৮৫.
A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?
  1. ক
    18
  2. খ
    27
  3. গ
    30
  4. ঘ
    35
সঠিক উত্তর: গ
30
উত্তর
সঠিক উত্তর: গ
30
গ
ব্যাখ্যা

Question: A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

Solution:
দেওয়া আছে:
মোট লোক = 45 জন
নির্ধারিত সময় = 40 দিন
10 দিনে সম্পন্ন কাজ = 1/6 অংশ

ধরি, সম্পূর্ণ কাজ = 1 একক

45 জন লোক 10 দিনে করে = 1/6 অংশ কাজ
∴ 45 জন লোক 1 দিনে করে = (1/6) ÷ 10 = 1/60 অংশ
∴ 1 জন লোক 1 দিনে করে = (1/60) ÷ 45 = 1/2700 অংশ

অবশিষ্ট কাজ = 1 - 1/6 = 5/6 অংশ
অবশিষ্ট সময় = 40 - 10 = 30 দিন

∴ অবশিষ্ট 5/6 অংশ কাজ 30 দিনে করতে হবে

∴ প্রতিদিনের প্রয়োজনীয় কাজের হার = (5/6) ÷ 30 অংশ
= 5/180 = 1/36 অংশ

এখন,
প্রতিদিন 1/2700 অংশ কাজ করে 1 জন
∴ 1 অংশ কাজ করে = 1 ÷ (1/2700) জন
∴ 1/36 অংশ কাজ করে = (2700/36) জন
= 75 জন

∴ অতিরিক্ত লোকের প্রয়োজন = 75 - 45 = 30 জন

৬৮৬.
Jishan and Akash can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days Akash had to leave and Jishan alone completed the remaining work. The whole work was completed in :
  1. ক
    ক) 10 days
  2. খ
    খ) 12 days
  3. গ
    গ) 14 days
  4. ঘ
    ঘ) 16 days
সঠিক উত্তর: খ
খ) 12 days
উত্তর
সঠিক উত্তর: খ
খ) 12 days
খ
ব্যাখ্যা
(Jishan + Akash)'s 1 day's work =1/15 + 1/10 
                                                  = (2 + 3)/30
                                                  = 5/30
                                                  = 1/6
(Jishan + Akash)'s 2 day's work = (1/6) ×2 = 1/3


Remaining work = 1 - 1/3 =(3 - 1)/3 = 2/3

1/15 work is done by Jishan in 1 day
2/3 work will be done by a in = 15 × (2/3) = 10 days

The total time taken = (10 + 2) = 12 days.
৬৮৭.
Akash can do a piece of work in 30 days. He works at it for 6 days and then Rakib finishes it in 18 days. In what time can Akash and Rakib together finish the work?
  1. ক
    ক) 90/7 days
  2. খ
    খ) 8 days
  3. গ
    গ) 12 days
  4. ঘ
    ঘ) 90/11 days
সঠিক উত্তর: ক
ক) 90/7 days
উত্তর
সঠিক উত্তর: ক
ক) 90/7 days
ক
ব্যাখ্যা
Question:  Akash can do a piece of work in 30 days. He works at it for 6 days and then Rakib finishes it in 18 days. In what time can Akash and Rakib together finish the work?

Solution: 
আকাশ ৩০ দিনে করে সম্পূর্ণ অংশ 
১ দিনে করে ১/৩০ অংশ 
৬ দিনে করে ৬/৩০ অংশ 
= ১/৫ অংশ 

বাকি থাকে ১ - ১/৫ অংশ 
= ৪/৫ অংশ 

রাকিব ১৮ দিনে করে ৪/৫ অংশ 
১ দিনে করে ২/৪৫ অংশ 

রাকিব ও আকাশ ১ দিনে করে (১/৩০) + (২/৪৫) অংশ 
= (৩ + ৪)/৯০ 
= ৭/৯০ 

সম্পুর্ণ কাজ করতে সময় লাগে = ৯০/৭ দিন
৬৮৮.
A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?
  1. ক
    8 boys
  2. খ
    10 boys
  3. গ
    13 boys
  4. ঘ
    15 boys
সঠিক উত্তর: গ
13 boys
উত্তর
সঠিক উত্তর: গ
13 boys
গ
ব্যাখ্যা
Question: A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?

Solution: 
(1 man + 1 woman)'s 1 day's work
= 1/6 + 1/9
= 5/18
Remaining work=(1 − 5/18)
=13/18

Work done by 1 boy in 1 day = 1/18

∴Number of boys required= (13×18)/18 boys
=13 boys
৬৮৯.
A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?
  1. ক
    6 days
  2. খ
    7 days
  3. ঘ
    9 days
সঠিক উত্তর: গ
উত্তর
সঠিক উত্তর: গ
গ
ব্যাখ্যা
Question: A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?

Solution:
৬৯০.
X, Y, and Z are hired to complete a project for Tk. 6900. X and Y together complete 17/25 of the work, and Y and Z together complete 13/25 of the work. What is the wage of Y in Taka?
  1. ক
    Tk. 1380
  2. খ
    Tk. 1460
  3. গ
    Tk. 1650
  4. ঘ
    Tk. 1250
সঠিক উত্তর: ক
Tk. 1380
উত্তর
সঠিক উত্তর: ক
Tk. 1380
ক
ব্যাখ্যা

Question: X, Y, and Z are hired to complete a project for Tk. 6900. X and Y together complete 17/25 of the work, and Y and Z together complete 13/25 of the work. What is the wage of Y in Taka?

Solution:
X + Y = 17/25
Y + Z = 13/25

অতএব,
X + Y + Y + Z = (17/25) + (13/25)
= 30/25

যেখানে, X + Y + Z = 1 (সম্পূর্ণ কাজ)

এখন,
(X + Y + Z + Y) - (X + Y + Z) = 30/25 - 1
∴ Y = 5/25 = 1/5

∴ Y এর বেতন = (1/5) × 6900 = Tk. 1380

৬৯১.
A factory produces 180 items in 2 days working 9 hours per day. How many items would it produce in 9 days working 10 hours per day? 
  1. ক
    1200 items
  2. খ
    500 items
  3. গ
    900 items
  4. ঘ
    700 items
সঠিক উত্তর: গ
900 items
উত্তর
সঠিক উত্তর: গ
900 items
গ
ব্যাখ্যা

Question: A factory produces 180 items in 2 days working 9 hours per day. How many items would it produce in 9 days working 10 hours per day?

Solution: 
180 items in 2 days, working 9 hours per day
Total hours worked = 2 × 9 = 18 hours
So, production rate = (180/18) = 10 items/hour

Total hours for 9 days working 10 hours/day
= 9 × 10 = 90 hours

So, total items = 90 × 10 = 900 items

৬৯২.
A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
  1. ক
    30 days
  2. খ
    40 days
  3. গ
    60 days
  4. ঘ
    70 days
সঠিক উত্তর: গ
60 days
উত্তর
সঠিক উত্তর: গ
60 days
গ
ব্যাখ্যা
Question: A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?

Solution:
Let,
A's 1 day'swork = x
and B's 1 day's work = y
Then, x + y = 1/30 ...........(1)

And,
16x + 44y = 1 ...........(2)

From (2) - (1) × 16 we get,
16x + 44y - 16x - 16y = 1 - 16/30
⇒ 28y = 14/30
⇒ y = 1/60

∴ B's 1 day's work is 1/60
∴ B can finish the whole work in 60 days
৬৯৩.
Mr. Jamal employed 50 workers to finish a work within 30 days. After 20 days he found out that only 50% work had been completed. How many additional workers would be needed to finish the task in scheduled time?
  1. ক
    ক) 40
  2. খ
    খ) 50
  3. গ
    গ) 80
  4. ঘ
    ঘ) None
সঠিক উত্তর: খ
খ) 50
উত্তর
সঠিক উত্তর: খ
খ) 50
খ
ব্যাখ্যা

এখানে দিন বাকি = 30 - 20 = 10 দিন এবং কাজ বাকি = 1 - 1/2 = 1/2অংশ
20 দিনে একটি কাজের 1/2 অংশ সম্পন্ন করে 50 জন
শ্রমিক
1 দিনে একটি কাজের 1/2 অংশ সম্পন্ন করে (50×20) = 1000 জন শ্রমিক
10 দিনে একটি কাজের 1/2 অংশ সম্পন্ন করে 1000/10 জন = 100 জন
সুতরাং অতিরিক্ত শ্রমিক লাগবে = 100 - 50 = 50 জন।

৬৯৪.
A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more  after 35 days and completes the work in stipulated time. If he had not  engaged  the additional men, how many days  behind schedule would it be finished?
  1. ক
    3 days
  2. খ
    5 days
  3. গ
    6 days
  4. ঘ
    9 days
সঠিক উত্তর: খ
5 days
উত্তর
সঠিক উত্তর: খ
5 days
খ
ব্যাখ্যা
Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more  after 35 days and completes the work in stipulated time. If he had not  engaged  the additional men, how many days  behind schedule would it be finished?

Solution:
[(100 × 35) + (200 × 5)]men can finish the work in 1 day
Therefore,
4500 men can finish the work in 1 day.
100 men can finish it in 4500/100 = 45 days.

∴ This is 5 days behind Schedule
৬৯৫.
Running at the same constant rate, 8 identical machines can produce a total of 320 bottles per minute. At this rate, how many bottles could 15 such machines produce in 6 minutes?
  1. ক
    3400 bottles
  2. খ
    3550 bottles
  3. গ
    3600 bottles
  4. ঘ
    3800 bottles
  5. ঙ
    None
সঠিক উত্তর: গ
3600 bottles
উত্তর
সঠিক উত্তর: গ
3600 bottles
গ
ব্যাখ্যা
Question: Running at the same constant rate, 8 identical machines can produce a total of 320 bottles per minute. At this rate, how many bottles could 15 such machines produce in 6 minutes?

Solution:
Given,
In 1 minute, 8 machines can produce 320 bottles
In 1 minute, 1 machines can produce 320/8 bottles
So, in 6 minute, 15 machines can produce = (320 × 6 × 15)/8 bottles
= 3600 bottles
৬৯৬.
Rihan can write 120 pages in 30 hours. Zayan and Rihan together can write 240 pages in 40 hours. In what time can Zayan write 60 pages? 
  1. ক
    33 hours
  2. খ
    24 hours
  3. গ
    20 hours
  4. ঘ
    30 hours
  5. ঙ
    40 hours
সঠিক উত্তর: ঘ
30 hours
উত্তর
সঠিক উত্তর: ঘ
30 hours
ঘ
ব্যাখ্যা

Question: Rihan can write 120 pages in 30 hours. Zayan and Rihan together can write 240 pages in 40 hours. In what time can Zayan write 60 pages?

Solution:
Given,
In 30 hours Rihan can write 120 pages
∴ In 1 hour Rihan can write 120 ÷ 30 = 4 pages

Rihan and Zayan together can write 240 ÷ 40 = 6 pages per hour

∴ Zayan's 1 hour work = (Rihan + Zayan)'s 1 hour work - Rihan's 1 hour work
= 6 - 4 = 2 pages/hour

Zayan's time:
2 pages in 1 hour
∴ 1 page in 1/2 hour
∴ 60 pages in (1 × 60) ÷ 2
= 30 hours

৬৯৭.
P can complete a piece of work in 18 days, while Q can complete the same work in 36 days. If both P and Q work together, in how many days will they be able to complete the entire work?
  1. ক
    18 days
  2. খ
    12 days
  3. গ
    36 days
  4. ঘ
    6 days
সঠিক উত্তর: খ
12 days
উত্তর
সঠিক উত্তর: খ
12 days
খ
ব্যাখ্যা
Question: P can complete a piece of work in 18 days, while Q can complete the same work in 36 days. If both P and Q work together, in how many days will they be able to complete the entire work?

Solution:
Given that,
P can do a piece of the work in 18 days and Q can do same work in 36 days

Now,
Let the total work = LCM(18, 36) = 36

Hence, total work = 36 units

Thus,
P does each day = 36 ÷ 18 = 2 units
Q does each day = 36 ÷ 36 = 1 unit

Hence, time taken by them to finish the work together = 36 ÷ (1 + 2) = 12 days.

∴ In 12 days working together they will complete the entire work.
৬৯৮.
Printer P, Printer Q and Printer R can print a batch of flyers in 4,8 and 16 hours respectively. How many Printer R are needed with One Printer P and three Printer Q to complete the lot in 1 hour?
  1. ক
    12
  2. খ
    8
  3. গ
    6
  4. ঘ
    3
সঠিক উত্তর: গ
6
উত্তর
সঠিক উত্তর: গ
6
গ
ব্যাখ্যা

Question: Printer P, Printer Q and Printer R can print a batch of flyers in 4,8 and 16 hours respectively. How many Printer R are needed with One Printer P and three Printer Q to complete the lot in 1 hour?

Solution: 
Here, Total work LCM(4, 8, 16) = 16 units
So, Efficiency of P = 4, Q = 2 and R = 1

Let, x number of Printer R required to complete the lot in 1 hour.
Now,
16 = (1 × 4 + 3 × 2) + 1 × x
⇒ 16 = 10 + x
⇒ x = 16 - 10
∴ x = 6 

Thus, 6 Printer R are needed.

৬৯৯.
In a camp, provisions are sufficient for 200 persons for 35 days. After 20 days, 50 persons depart. Determine the number of days the remaining food will last.
  1. ক
    10 days
  2. খ
    15 days
  3. গ
    20 days
  4. ঘ
    25 days
সঠিক উত্তর: গ
20 days
উত্তর
সঠিক উত্তর: গ
20 days
গ
ব্যাখ্যা

Question: In a camp, provisions are sufficient for 200 persons for 35 days. After 20 days, 50 persons depart. Determine the number of days the remaining food will last.

Solution:
10 দিন পর 50 জন চলে যাওয়ায়,
অবশিষ্ট দিন = (35 - 20) = 15 দিন 
এবং অবশিষ্ট লোক = (200 - 50) = 150 জন  

এখন, 
হোস্টেলে 200 জনের  খাদ্য মজুদ আছে = 15 দিনের 
∴ 1 জনের  খাদ্য মজুদ আছে = (15 × 200) দিনের
∴ 150 জনের  খাদ্য মজুদ আছে = (15 × 200)/150 দিনের = 20 দিনের

৭০০.
A certain number of men can complete a piece of work in 180 days. If there are 30 men less, it will take 20 days more for the work to be completed. How many men were there originally?
  1. ক
    135
  2. খ
    165
  3. গ
    150
  4. ঘ
    180
  5. ঙ
    300
সঠিক উত্তর: ঙ
300
উত্তর
সঠিক উত্তর: ঙ
300
ঙ
ব্যাখ্যা
Question: A certain number of men can complete a piece of work in 180 days. If there are 30 men less, it will take 20 days more for the work to be completed. How many men were there originally?

Solution:
Let there be x men originally.
They were to complete the work in 180 days but as the number of persons is reduced to x - 30.
∴ Work takes 20 more days.

So the equation is
180x = (x - 30)200
⇒ 180x = 200x - 6000
⇒ 20x = 6000
⇒ x = 300