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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 ১০ / ১১ · ৯০১–১,০০০ / ১,০৭৬

৯০১.
In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 8 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
  1. ক
    30
  2. খ
    45
  3. গ
    60
  4. ঘ
    90
সঠিক উত্তর: গ
60
উত্তর
সঠিক উত্তর: গ
60
গ
ব্যাখ্যা

Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 8 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?

Solution:
Let,
total distance x kilometers

ATQ,
x/5 + 2x/3 + 8 = x
⇒ x - x/5 - 2x/3 = 8
⇒ (15x - 3x - 10x)/15 = 8
⇒ 2x = 120
∴ x = 60

৯০২.
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
    90/7 days
  2. খ
    90/4 days
  3. গ
    90/11 days
  4. ঘ
    90 days
সঠিক উত্তর: ক
90/7 days
উত্তর
সঠিক উত্তর: 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 
৯০৩.
Sina and Sium are preparing a report. Sina takes 8 hours to write 48 pages on a computer, while Sium takes 7 hours to write 42 pages. How much time will it take, working together on two different computers, to write a report of 132 pages?
  1. ক
    9 hours
  2. খ
    10 hours
  3. গ
    11 hours
  4. ঘ
    12 hours
সঠিক উত্তর: গ
11 hours
উত্তর
সঠিক উত্তর: গ
11 hours
গ
ব্যাখ্যা
Question: Sina and Sium are preparing a report. Sina takes 8 hours to write 48 pages on a computer, while Sium takes 7 hours to write 42 pages. How much time will it take, working together on two different computers, to write a report of 132 pages?

Solution:
Sina takes 8 hours to write 48 pages.
So, Sina writes in 1 hour = 48/8 = 6 pages

Sium takes 7 hours to write 42 pages.
So, Sium writes in 1 hour = 42/7 = 6 pages.

Together, Sina and Sium write in 1 hour = 6 + 6 = 12 pages

Now, Time taken to write 1 page = 1/12 hours
Time taken to write 132 pages = (1/12) × 132 hours
= 11
৯০৪.
40 workers can build 40 engines working 6 hours a day. How many workers need to be appointed extra to boost the production to double if they work 8 hours a days?
  1. ক
    15 workers
  2. খ
    10 workers
  3. গ
    20 workers
  4. ঘ
    25 workers
সঠিক উত্তর: গ
20 workers
উত্তর
সঠিক উত্তর: গ
20 workers
গ
ব্যাখ্যা
Question: 40 workers can build 40 engines working 6 hours a day. How many workers need to be appointed extra to boost the production to double if they work 8 hours a days?

Solution:
6 hours to build 40 engines by 50 workers
1 hour to build 1 engine by = (40 × 6)/40 workers
8 hours to build 80 engine by = (6 × 80)/8 workers
= 60 workers

∴ extra workers = 60 - 40 = 20 workers 
৯০৫.
A team of 3 men and 4 women can complete 1/3 of a job in 4 days. After that, 2 more women join the team and they complete the next 1/3 of the job in 3 days. How many women can complete the whole job in 6 days?
  1. ক
    10 women
  2. খ
    12 women
  3. গ
    16 women
  4. ঘ
    8 women
  5. ঙ
    None of these
সঠিক উত্তর: খ
12 women
উত্তর
সঠিক উত্তর: খ
12 women
খ
ব্যাখ্যা
Question: A team of 3 men and 4 women can complete 1/3 of a job in 4 days. After that, 2 more women join the team and they complete the next 1/3 of the job in 3 days. How many women can complete the whole job in 6 days?

Solution:
Let,
Men = M, Women = W
3M & 4W complete in 4 days = 1/3 part of the job
∴ 3M & 4W complete in 1 days = 1/12 part of the job

After joining 2 women,
3M & 6W complete in 3 days= 1/3 part of the job
3M & 6W complete in 1 days= 1/9 part of the job

Now,
2 women can complete in 1 day = (1/9) - (1/12) = (4 - 3)/36 = 1/36
∴ 1 women can complete in 1 day = 1/72
∴ 1 women dose 1(whole) of the job in = 1 × 72 = 72 day

∴ In 72 days the job completed by 1 women
∴ In 1 days the job completed by = 1 × 72 women
∴ In 6 days the job completed by = 72/6 = 12 women
৯০৬.
A college hostel mess has provisions for 25 days for 350 boys. At the end of 10 days, when some boys were shifted to another hostel, it was found that now the provisions will last for 21 more days. How may boys were shifted to another hostel?
  1. ক
    92
  2. খ
    110
  3. গ
    98
  4. ঘ
    100
সঠিক উত্তর: ঘ
100
উত্তর
সঠিক উত্তর: ঘ
100
ঘ
ব্যাখ্যা
Question: A college hostel mess has provisions for 25 days for 350 boys. At the end of 10 days, when some boys were shifted to another hostel, it was found that now the provisions will last for 21 more days. How may boys were shifted to another hostel?

Solution:
A college hostel mess has provisions for 25 days for 350 boys.
At the end of 10 days, when some boys were shifted to another hostel, it was found that now the provisions will last for 21 more days.

Available provisions = 25 × 350 = 8750 units
After 10 days the remaining provision = 8750 - 10 × 350 ⇒ 5250 units

Let N number of boys shifted to another hostel.
According to the question,
(350 - N) × 21 = 5250
⇒ 350 - N = 5250/21
⇒ 350 - N = 250
⇒ N = 350 - 250
⇒ N = 100

∴ 100 boys were shifted to another hostel.
৯০৭.
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
    Tk. 50
  2. খ
    Tk. 30
  3. গ
    Tk. 40
  4. ঘ
    Tk. 60
সঠিক উত্তর: গ
Tk. 40
উত্তর
সঠিক উত্তর: গ
Tk. 40
গ
ব্যাখ্যা
Man = 3 boy
Daily wages for them = 800/5
 = 160
4 boy (3 Boy + 1 Boy) = 160
4 boy = 160
Or, boy = Tk. 40
৯০৮.
X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?
  1. ক
    5/12
  2. খ
    1/6
  3. গ
    7/12
  4. ঘ
    3/10
সঠিক উত্তর: গ
7/12
উত্তর
সঠিক উত্তর: গ
7/12
গ
ব্যাখ্যা
Question: X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?

Solution:
The work rate of X is 1/12 (since X can complete the work in 12 days).
The work rate of Y is 1/18 (since Y can complete the work in 18 days).
In 3 days they complete = 3{(1/12) + (1/18)}
= 3 × (5/36)
= 5/12

Then the fraction of work that is left is = 1 - (5/12)
= (12 - 5)/12
= 7/12
৯০৯.
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
    ক) 3
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 9
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: খ
খ) 5
উত্তর
সঠিক উত্তর: খ
খ) 5
খ
ব্যাখ্যা
[(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
৯১০.
Rafi and Shafi can paint a room in 4 days. Shafi can do it alone in 6 days. How many days will Rafi take to paint the room alone?
  1. ক
    12 days
  2. খ
    10 days
  3. গ
    15 days
  4. ঘ
    9 days
সঠিক উত্তর: ক
12 days
উত্তর
সঠিক উত্তর: ক
12 days
ক
ব্যাখ্যা

Question: Rafi and Shafi can paint a room in 4 days. Shafi can do it alone in 6 days. How many days will Rafi take to paint the room alone?

Solution:
ধরা যাক,
Rafi একা কাজটি করতে x দিন সময় নেন।
∴ Rafi-র 1 দিনের কাজ = 1/x
∴ Shafi-র 1 দিনের কাজ = 1/6 (কারণ সে একা ৬ দিনে কাজটি করে)

তারা দুজনে মিলে ৪ দিনে কাজ শেষ করে।
∴ তাদের 1 দিনের একত্রে কাজ = 1/4

এখন,
(1/x) + (1/6) = 1/4
⇒ (6 + x) / (6x) = 1/4
⇒ 4(6 + x) = 6x
⇒ 24 + 4x = 6x
⇒ 24 = 6x - 4x = 2x
⇒ x = 24 / 2 = 12

∴ Rafi একা কাজটি করতে 12 দিন সময় নেবে।

৯১১.
If |x + 2| ≤ 6, then which of the following intervals represents all possible values of the expression 3x - 4 ?
  1. ক
    [- 28, 8]
  2. খ
    [- 24, 12]
  3. গ
    [- 18, 10]
  4. ঘ
    [- 14, 6]
  5. ঙ
    [- 10, 4]
সঠিক উত্তর: ক
[- 28, 8]
উত্তর
সঠিক উত্তর: ক
[- 28, 8]
ক
ব্যাখ্যা

Question: If |x + 2| ≤ 6, then which of the following intervals represents all possible values of the expression 3x - 4 ?

Solution:
|x + 2| ≤ 6
⇒ - 6 ≤ x + 2 ≤ 6
⇒ - 6 - 2 ≤ x + 2 - 2 ≤ 6 - 2
⇒ - 8 ≤ x ≤ 4
⇒ - 24 ≤ 3x ≤ 12
⇒ - 24 - 4 ≤ 3x - 4 ≤ 12 - 4
⇒ - 28 ≤ 3x - 4 ≤ 8

∴ All possible values of 3x - 4 lie in the interval [- 28, 8].

৯১২.
A man and a boy can finish a job working together for 6 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?
  1. ক
    ক) 5
  2. খ
    খ) 6
  3. গ
    গ) 9
  4. ঘ
    ঘ) 10
সঠিক উত্তর: গ
গ) 9
উত্তর
সঠিক উত্তর: গ
গ) 9
গ
ব্যাখ্যা
Question: A man and a boy can finish a job working together for 6 days. The man can work as much as two boys can do. Then in how many days can the man do it alone?

Solution: 
1 man and 1 boy can do in 1 day 1/6 part
2 man and 2 boy can do in 1 day 2/6 part = 1/3 part

Now 1 man = 2 boys 
(2 + 1) man can do in 1 day is 1/3 part
3 man can do in 1 day is 1/3 part
1 man can do in 1 day is 1/(3 × 3) part = 1/9 part

∴ Man alone can do the work in 9 days
৯১৩.
Ellmi bought 5 pints of frozen yogurt and a tray of jumbo shrimp from The Food Place for a total of Tk. 4500. If the price of a tray of jumbo shrimp is Tk. 2500, what is the price of a pint of frozen yogurt?
  1. ক
    Tk. 400
  2. খ
    Tk. 500
  3. গ
    Tk. 900
  4. ঘ
    Tk. 1400
সঠিক উত্তর: ক
Tk. 400
উত্তর
সঠিক উত্তর: ক
Tk. 400
ক
ব্যাখ্যা
Question: Ellmi bought 5 pints of frozen yogurt and a tray of jumbo shrimp from The Food Place for a total of Tk. 4500. If the price of a tray of jumbo shrimp is Tk. 2500, what is the price of a pint of frozen yogurt?

Solution:
Ellmi bought 5 pints of frozen yogurt and a shrimp tray.
We can use x to represent price of a pint of frozen yogurt.
The price of 5 pints of frozen yogurt, then, is  5x

The price of a shrimp tray is 2500
Ellmi spent a total of Tk. 4500, which is the sum of 5x and 2500. We can now write an equation and solve it:
5x + 2500 = 4500
⇒ 5x = 2000
∴ x = 400
৯১৪.
X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?
  1. ক
    3/10
  2. খ
    1/6
  3. গ
    5/12
  4. ঘ
    7/12
সঠিক উত্তর: ঘ
7/12
উত্তর
সঠিক উত্তর: ঘ
7/12
ঘ
ব্যাখ্যা

Question: X can complete a task in 12 days and Y in 18 days. If they work together for 3 days, what fraction of work is left?

Solution:
The work rate of X is 1/12 (since X can complete the work in 12 days).
The work rate of Y is 1/18 (since Y can complete the work in 18 days).
In 3 days they complete = 3{(1/12) + (1/18)}
= 3 × (5/36)
= 5/12

Then the fraction of work that is left is = 1 - (5/12)
= (12 - 5)/12
= 7/12

৯১৫.
What is the maximum number of half-point bottles of cream that can be filled with a 4- gallon can of cream? (2 pt. = 1 qt. and 4 qt. = 1 gal)
  1. ক
    ক) 16
  2. খ
    খ) 24
  3. গ
    গ) 30
  4. ঘ
    ঘ) 64
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: ঘ
ঘ) 64
উত্তর
সঠিক উত্তর: ঘ
ঘ) 64
ঘ
ব্যাখ্যা
Question: What is the maximum number of half-point bottles of cream that can be filled with a 4- gallon can of cream? (2 pt. = 1 qt. and 4 qt. = 1 gal)

Solution:
The given information:
1 gallon (gal) = 4 quarts (qt)
1 quart (qt) = 2 pints (pt)
1 pint (pt) = 2 half-pints

∴1 gallon = 4 quarts = 8 pints =16 half-pints.

∴ 4 gallons = 4 × 16 half-pints = 64 half-pints

Therefore, the maximum number of half-pint bottles of cream that can be filled with a 4-gallon can of cream is 64 half-pints.
৯১৬.
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
    150
  2. খ
    165
  3. গ
    180
  4. ঘ
    300
সঠিক উত্তর: ঘ
300
উত্তর
সঠিক উত্তর: ঘ
300
ঘ
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.
৯১৭.
If 20 workers can complete a road construction in 45 days by working 6 hours a day, how many workers are required to complete the same construction in 30 days by working 9 hours a day?
  1. ক
    15 workers
  2. খ
    20 workers
  3. গ
    30 workers
  4. ঘ
    25 workers
সঠিক উত্তর: খ
20 workers
উত্তর
সঠিক উত্তর: খ
20 workers
খ
ব্যাখ্যা
Question: If 20 workers can complete a road construction in 45 days by working 6 hours a day, how many workers are required to complete the same construction in 30 days by working 9 hours a day?

Solution:
দৈনিক ৬ ঘণ্টা কাজ করে ৪৫ দিনে একটি কাজ সম্পন্ন করে ২০ জন
দৈনিক ১ ঘণ্টা কাজ করে ৪৫ দিনে একটি কাজ সম্পন্ন করে ২০ × ৬ জন
দৈনিক ১ ঘণ্টা কাজ করে ১ দিনে একটি কাজ সম্পন্ন করে ১২০ × ৪৫ জন
দৈনিক ৯ ঘণ্টা কাজ করে ১ দিনে একটি কাজ সম্পন্ন করে (১২০ × ৪৫)/৯  জন
দৈনিক ৯ ঘণ্টা কাজ করে ৩০ দিনে একটি কাজ সম্পন্ন করে (১২০ × ৪৫)/(৯ × ৩০) জন
= ২০ জন
৯১৮.
A group of men decided to do a job in 5 days. But since 10 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?
  1. ক
    145
  2. খ
    115
  3. গ
    105
  4. ঘ
    90
সঠিক উত্তর: গ
105
উত্তর
সঠিক উত্তর: গ
105
গ
ব্যাখ্যা
Question: A group of men decided to do a job in 5 days. But since 10 men dropped out every day, the job completed at the end of the 7th day. How many men were there at the beginning?

Solution: 
Let X be the initial number of men then,
According to the question,
5X = X + (X - 10) + (X - 20) + (X - 30) + (X - 40) + (X - 50) + (X - 60)
or, 5X = 7X - 210
or, 2X = 210
or, X = 210/2
or, X = 105
৯১৯.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 13
সঠিক উত্তর: গ
গ) 12
উত্তর
সঠিক উত্তর: গ
গ) 12
গ
ব্যাখ্যা

Let the required number of working hours per day be x
More pumps, Less working hours per day (Indirect proportion)
Less days, More working hours per day (Indirect proportion)
Pumps 4:3 & Days 1:2 } :: 8:x
∴ 4×1×x = 3×2×8
⇔ x = (3×2×8)/(4)
⇔ x = 12

৯২০.
Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?
  1. ক
    ক) 5 : 2
  2. খ
    খ) 4 : 3
  3. গ
    গ) 2 : 3
  4. ঘ
    ঘ) 3 : 2
সঠিক উত্তর: খ
খ) 4 : 3
উত্তর
সঠিক উত্তর: খ
খ) 4 : 3
খ
ব্যাখ্যা
(20 × 16) women can complete the work in 1 day
1 woman's 1day's work = 1/ 320
(16 × 15) men can complete the work in 1 day
1 man's 1day's work = 1/240
So, required ratio = 1/240 : 1/320
= 1/3 : 1/4
= 4:3
৯২১.
Tina works four times as fast as Rina. If Rina can complete a work in 20 days alone, how many days will Tina and Rina together take to complete the work? 
  1. ক
    2 days 
  2. খ
    4 days 
  3. গ
    5 days 
  4. ঘ
    6 days 
  5. ঙ
    None
সঠিক উত্তর: খ
4 days 
উত্তর
সঠিক উত্তর: খ
4 days 
খ
ব্যাখ্যা

Question: Tina works four times as fast as Rina. If Rina can complete a work in 20 days alone, how many days will Tina and Rina together take to complete the work?

Solution:
Tina : Rina work ratio = 4 : 1
∴ Time taken ratio = 1 : 4

Since Rina takes 20 days, Tina takes = 20 / 4 = 5 days

∴ (Tina + Rina)'s 1 day work = (1/5) + (1/20)
= (4 + 1)/20
= 5/20
= 1/4

∴ Total days to finish the work = 1 ÷ (1/4) = 4 days

∴ Tina and Rina together can complete the work in 4 days.

৯২২.
Two men can do a piece of work in x days. But y women can do that in 3 days. Then the ratio of the work done by 1 man and 1 woman is?
  1. ক
    ক) 3y : 2x
  2. খ
    খ) 2x : 3y
  3. গ
    গ) 2x : y
  4. ঘ
    ঘ) 2y : 3x
সঠিক উত্তর: ক
ক) 3y : 2x
উত্তর
সঠিক উত্তর: ক
ক) 3y : 2x
ক
ব্যাখ্যা

2 men can do a work in x days
1 men can do a work in (2 × x) days
y women can do a work in 3 days
1 women can do a work in 3y days
1 man : 1 woman
Days - 2x : 3y
Efficiency - 3y : 2x

৯২৩.
Lopa can do a work in 3 days while Rasel can do the same work in 2 days. Both of them finish the work together and get Tk. 150. What is the share of Lopa?
  1. ক
    ক) Tk. 30
  2. খ
    খ) Tk. 60
  3. গ
    গ) Tk. 70
  4. ঘ
    ঘ) Tk. 75
সঠিক উত্তর: খ
খ) Tk. 60
উত্তর
সঠিক উত্তর: খ
খ) Tk. 60
খ
ব্যাখ্যা

Lopa's wages : Rasel's wages
= Lopa's 1 day's work : Rasel's 1 day's work
= 1/3 : 1/2
= 2 : 3
∴ Lopa's share = Tk.(2/5) × 150
= Tk 60.

৯২৪.
A machine produces 240 toys in 4/3 hours. How many toys can it produce in 25 minutes?
  1. ক
    60 toys
  2. খ
    75 toys
  3. গ
    80 toys
  4. ঘ
    90 toys
সঠিক উত্তর: খ
75 toys
উত্তর
সঠিক উত্তর: খ
75 toys
খ
ব্যাখ্যা

Question: A machine produces 240 toys in 4/3 hours. How many toys can it produce in 25 minutes?

Solution:
Given,
Time = 4/3 hours = (4/3) × 60 = 80 minutes

In 80 minutes, the number of toys produced = 240
In 1 minute, the number of toys produced = 240/80 = 3
In 25 minutes, the number of toys produced  = 3 × 25 = 75

∴ The machine can produce 75 toys in 25 minutes.

৯২৫.
If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?
  1. ক
    175 hectares
  2. খ
    225 hectares
  3. গ
    250 hectares
  4. ঘ
    275 hectares
  5. ঙ
    None of these
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:
Let the required number of hectares be x.

More men (↑) More hectares (↑)

⇒ 8 × 12 × x = 30 × 20 × 40
⇒ x = (30 × 20 × 40)/(8 × 12)
∴ x = 250
৯২৬.
If 12 men work on a particular task. It takes them 24 days to complete it. On the other hand 12 women can complete the same task in 12 days. How many days would it take if the 12 man and 12 women complete with each other to finish the same task?
  1. ক
    ক) 5 days
  2. খ
    খ) 6days
  3. গ
    গ) 8 days
  4. ঘ
    ঘ) 16 days
সঠিক উত্তর: গ
গ) 8 days
উত্তর
সঠিক উত্তর: গ
গ) 8 days
গ
ব্যাখ্যা

12 জন পুরুষ 24 দিনে করে 1 অংশ
∴ 12 জন পুরুষ 1 দিনে করে 1/24 অংশ
আবার, 12 জন মহিলা 12 দিনে করে 1 অংশ
∴ 12 জন মহিলা 1 দিনে করে 1/12 অংশ
তাহলে, 12 জন পুরুষ ও 12 জন মহিলা 1 দিনে করে
= (1/24 + 1/12) অংশ
= (1+2)/24 অংশ
= 3/24 = 1/8অংশ

নারী এবং পুরুষেরা একত্রে 1/8 অংশ করে 1 দিনে
∴ তারা একত্রে 1 বা সম্পূর্ণ অংশ করে 1×8 = 8 দিনে

৯২৭.
In a queue, Shahadat is ninth from the rear end. Altaf's place is eighth from the front. Nitu is standing between the two. What could be the minimum number of boys standing in the queue?
  1. ক
    ক) 18
  2. খ
    খ) 14
  3. গ
    গ) 22
  4. ঘ
    ঘ) 24
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: খ
খ) 14
উত্তর
সঠিক উত্তর: খ
খ) 14
খ
ব্যাখ্যা

1 2 3 4 5 6 (Shahadat) 7 (Nitu) 8 (Altaf) 9 10 11 12 13 14
Here, Althaf is 8th from front, Shankar is 9th from rear end and Nitu is between them
So minimum no. of boys standing in the queue = 14.

৯২৮.
The average wages of a worker during a fortnight comprising 15 consecutive working days was ৳ 90 per day. During the first 7 days, his average wages was ৳ 87/day and the average wages during the last 7 days was ৳ 92/day. What was his wage on the 8th day?
  1. ক
    Tk. 80
  2. খ
    Tk. 72
  3. গ
    Tk. 54
  4. ঘ
    Tk. 97
সঠিক উত্তর: ঘ
Tk. 97
উত্তর
সঠিক উত্তর: ঘ
Tk. 97
ঘ
ব্যাখ্যা
The total wages earned during the 15 days that the worker worked ,
= 15 × 90
= ৳ 1350

The total wages earned during the first 7 days
= 7 × 87
= ৳ 609

The total wages earned during the last 7 days
= 7 × 92
= ৳ 644

Total wages earned during the 15 days,
= wages during first 7 days + wage on 8th day + wages during the last 7 days.
Therefore, 1350 = 609 + wage on 8th day + 644
or, wage on 8th day = 1350 - 609 - 644
                                 = ৳ 97
৯২৯.
Rina completes 60% or 3/5 of a work in 12 days. Then she calls in Sima, and together they finish the remaining work in 6 days. How long would Sima alone take to complete the whole work?
  1. ক
    45 days
  2. খ
    40 days
  3. গ
    50 days
  4. ঘ
    60 days
সঠিক উত্তর: ঘ
60 days
উত্তর
সঠিক উত্তর: ঘ
60 days
ঘ
ব্যাখ্যা

Question: Rina completes 60% or 3/5 of a work in 12 days. Then she calls in Sima, and together they finish the remaining work in 6 days. How long would Sima alone take to complete the whole work?

Solution:
Here,
Rina does 3/5 of the work in 12 days
in one day, she does = (3/5 ÷ 12)
= 3/60
= 1/20 part

In 6 days, she does 6/20 = 3/10 part
work remaining = 2/5

Together, they do 2/5 in 6 days
Together in one day = (2/5) ÷ 6
= 2/30
= 1/15

Rina one day = 1/20
Sima one day = 1/15 - 1/20
= (4-3)/60
= 1/60

∴ Sima alone will take 60 days to complete the whole work.

৯৩০.
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) 35
  2. খ
    খ) 40
  3. গ
    গ) 45
  4. ঘ
    ঘ) 50
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: খ
খ) 40
উত্তর
সঠিক উত্তর: খ
খ) 40
খ
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

৯৩১.
Painter A can paint a house in 16 days, and painter B can do the same work in 20 days. With the help of painter C, they paint the house in 8 days only. Then, Painter C alone can do this task in -
  1. ক
    ক) 80 Days
  2. খ
    খ) 85 Days
  3. গ
    গ) 79 Days
  4. ঘ
    ঘ) 76 Days
সঠিক উত্তর: ক
ক) 80 Days
উত্তর
সঠিক উত্তর: ক
ক) 80 Days
ক
ব্যাখ্যা
A paints in 20 days;
B paints in 30 days;
Let C paint in c days.

1/20 + 1/16 + 1/c = 1/8
 1/c = 1/8 – 1/20 – 1/16
1/c = (10 – 4 – 5)/80 = 1/80
Hence, C alone should paint the house in 80 days.
৯৩২.
One army camp had ration for 560 soldiers for 20 days, 560 soldiers reported for the camp, and after 12 days, 112 soldiers were sent to another camp. For how many days, the remaining soldiers can stay in the camp without getting any new ration?
  1. ক
    10 days
  2. খ
    12 days
  3. গ
    16 days
  4. ঘ
    14 days
সঠিক উত্তর: ক
10 days
উত্তর
সঠিক উত্তর: ক
10 days
ক
ব্যাখ্যা
Question: One army camp had ration for 560 soldiers for 20 days, 560 soldiers reported for the camp, and after 12 days, 112 soldiers were sent to another camp. For how many days, the remaining soldiers can stay in the camp without getting any new ration?

Solution:
After 12 days, there was ration for 560 soldiers for 8 days.
Remaining persons = (560-112) = 448
Less soldiers, more days (inverse proportion)
Let the x is the required number of days
Then, 448 : 560 = 8 : x
Or, x = (560 × 8)/ 448 = 10
Hence, the required number of days is 10.
৯৩৩.
If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?
  1. ক
    4x
  2. খ
    4x2
  3. গ
    x2
  4. ঘ
    16x2
সঠিক উত্তর: খ
4x2
উত্তর
সঠিক উত্তর: খ
4x2
খ
ব্যাখ্যা
Question: If each photocopy of a manuscript costs 4 cents per page, what is the cost, in cents, to reproduce x copies of an x-page manuscript?

Solution:
Cost to reproduce 1 page of a manuscript = 4 cents
∴ Cost to reproduce x pages of a manuscript= 4x cents

Cost to reproduce x copies of a x page manuscript= x × 4x cents = 4x2cents
৯৩৪.
A manager has Tk. 6000 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
    Tk. 750
  2. খ
    Tk. 1000
  3. গ
    Tk. 1200
  4. ঘ
    Tk. 1500
সঠিক উত্তর: গ
Tk. 1200
উত্তর
সঠিক উত্তর: গ
Tk. 1200
গ
ব্যাখ্যা
Question: A manager has Tk. 6000 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 = 1200
৯৩৫.
If 12 men or 18 women can do a work in 14 days, then in how many days will 8 men and 16 women do the same work?
  1. ক
    ক) 7 days
  2. খ
    খ) 8 days
  3. গ
    গ) 9 days
  4. ঘ
    ঘ) 6 days
সঠিক উত্তর: গ
গ) 9 days
উত্তর
সঠিক উত্তর: গ
গ) 9 days
গ
ব্যাখ্যা
Question: If 12 men or 18 women can do a work in 14 days, then in how many days will 8 men and 16 women do the same work?

Solution:
Let the required number of days be x.
12 men = 18 women
8 men = (18 × 8)/12 women = 12 women

Total women = (12 + 16) = 28

More women , Less days.
∴ 28 : 18 = 14 : x
⇒ 28/18 = 14/x
⇒ x = (18 × 14)/28
∴ x = 9

∴ Hence, required number of days = 9
৯৩৬.
There is food for 40 members for 30 days. How many days can 30 members survive with the same food?
  1. ক
    ক) 40 days
  2. খ
    খ) 35 days
  3. গ
    গ) 50 days
  4. ঘ
    ঘ) 60 days
সঠিক উত্তর: ক
ক) 40 days
উত্তর
সঠিক উত্তর: ক
ক) 40 days
ক
ব্যাখ্যা
Question: There is food for 40 members for 30 days. How many days can 30 members survive with the same food?

Solution: 
40 members have food for 30 days
1 member have food for (30 × 40) days
30 members have food for (30 × 40)/30 days
= 40 days
৯৩৭.
The cost of 8 fans and 14 ovens is Tk. 36520. What is the cost of 12 fans and 21 ovens ?
  1. ক
    ক) Tk. 82170
  2. খ
    খ) Tk. 36520
  3. গ
    গ) Tk. 54780
  4. ঘ
    ঘ) Tk.18260
সঠিক উত্তর: গ
গ) Tk. 54780
উত্তর
সঠিক উত্তর: গ
গ) Tk. 54780
গ
ব্যাখ্যা
Cost of 8 fan's and 14 oven's is Tk. 36520
Cost of 4 fan's and 7 oven's is Tk. 36520/2
  = Tk.18260
Cost of 12 fan's and 21 oven's is
= 18260 × 3
= Tk. 54780
৯৩৮.
M’s efficiency is three times N’s efficiency. M can finish a job in 60 days less than N. If they work together, then in how many days the job will be done.
  1. ক
    20 days
  2. খ
    22.5 days
  3. গ
    24.5 days
  4. ঘ
    30 days
সঠিক উত্তর: খ
22.5 days
উত্তর
সঠিক উত্তর: খ
22.5 days
খ
ব্যাখ্যা
Question: M’s efficiency is three times N’s efficiency. M can finish a job in 60 days less than N. If they work together, then in how many days the job will be done.

Solution:
Let the number of days N takes to finish the job be x days. Since M is three times as efficient as N, M will take x/3 days to finish the same job.
It is also given that M can finish the job in 60 days less than N, so-
x/3 = x - 60
⇒ x = 3(x - 60)
⇒ x = 3x - 180
⇒ 0 = 2x - 180
⇒ 2x = 180
∴ x = 90

So, N takes 90 days to do the job.
And N takes (90 ÷ 3) = 30 days to do the job.
M’s 1 day’s work = 1/30
N’s 1 day’s work = 1/90

(M + N)’s 1 day’s work =( 1/30 + 1/90) = 2/45
M and N together can do the job in 45/2 days = 22.5 days.
৯৩৯.
A woman and a child received 8400 Tk. as wages for 7 days for the work they did together. The woman's efficiency in the work was triple that of the child. What are the daily wages of the child?
  1. ক
    300 Tk
  2. খ
    600 Tk
  3. গ
    400 Tk
  4. ঘ
    800 Tk
সঠিক উত্তর: ক
300 Tk
উত্তর
সঠিক উত্তর: ক
300 Tk
ক
ব্যাখ্যা
Question: A woman and a child received 8400 Tk. as wages for 7 days for the work they did together. The woman's efficiency in the work was triple that of the child. What are the daily wages of the child?

Solution:
Ratio of 1 day's work of woman and child = 3 : 1
Total wages of the child = (8400 × 1/4)
= 2100 Tk.

∴ Daily wages of the child = 2100/7 = 300 Tk.
৯৪০.
If a quarter kg of potato costs 20 Tk, how much Tk will 200 gm cost?
  1. ক
    ক) 12 Tk
  2. খ
    খ) 15 Tk
  3. গ
    গ) 16 Tk
  4. ঘ
    ঘ) 18 Tk
সঠিক উত্তর: গ
গ) 16 Tk
উত্তর
সঠিক উত্তর: গ
গ) 16 Tk
গ
ব্যাখ্যা
Question: If a quarter kg of potato costs 20 Tk, how much Tk will 200 gm cost?

Solution:
A quarter of 1 kg = 1/4 kg
200 gram = 200/1000 = 1/5 kg

1/4 kg of potato's cost is 20 Tk
1 kg of potato's cost is 20 × 4 Tk
1/5 kg of potato's cost is (20 × 4)/5 Tk
= 16 Tk
৯৪১.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for 3200 Tk. With the help of C they completed the work in 3 days. How much is to be paid to C?
  1. ক
    ক) 1600 Tk.
  2. খ
    খ) 1200 Tk.
  3. গ
    গ) 600 Tk.
  4. ঘ
    ঘ) 400 Tk.
সঠিক উত্তর: ঘ
ঘ) 400 Tk.
উত্তর
সঠিক উত্তর: ঘ
ঘ) 400 Tk.
ঘ
ব্যাখ্যা
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for 3200 Tk. With the help of C they completed the work in 3 days. How much is to be paid to C?

Solution:
A ১ দিনে করে ১/৬ অংশ 
B ১ দিনে করে ১/৮ অংশ 

A, B, C ১ দিনে করে ১/৩ অংশ কাজ 

C ১ দিনে করে (১/৩) - (১/৬) - (১/৮)
= ১/২৪ অংশ 

তাদের কাজের অংশের অনুপাত = (১/৬) : (১/৮) : (১/২৪)
= ৪ : ৩ : ১ 

C পাবে = ৩২০০ × ১/(৪ + ৩ + ১)
= ৩২০০/৮ 
= ৪০০ টাকা 
৯৪২.
30 women can do a work in 15 days. 18 men can complete the same work in 10 days. What is the ratio between the capacity of a man and a woman?
  1. ক
    ক) 2 : 5
  2. খ
    খ) 2 : 3
  3. গ
    গ) 3 : 2
  4. ঘ
    ঘ) 5 : 2
সঠিক উত্তর: ঘ
ঘ) 5 : 2
উত্তর
সঠিক উত্তর: ঘ
ঘ) 5 : 2
ঘ
ব্যাখ্যা
Question: 30 women can do a work in 15 days. 18 men can complete the same work in 10 days. What is the ratio between the capacity of a man and a woman?

Solution:
( 30 × 15 ) women can complete the work in 1 day
1 woman's 1 day's work = 1/450

( 18 × 10 ) men can complete the work in 1 day
1 man's 1 day's work = 1/180

 So, required ratio = 1/180 : 1/450
 = 1/2 : 1/5 
= 5 : 2
৯৪৩.
10 men completed half of a work in 8 days. How many extra men should be added to finish the rest of the work within 4 days?
  1. ক
    ক) 5 men
  2. খ
    খ) 8 men
  3. গ
    গ) 10 men
  4. ঘ
    ঘ) 15 men
সঠিক উত্তর: গ
গ) 10 men
উত্তর
সঠিক উত্তর: গ
গ) 10 men
গ
ব্যাখ্যা
Question: 10 men completed half of a work in 8 days. How many extra men should be added to finish the rest of the work within 4 days?

Solution: 
অর্ধেক কাজ করার পর বাকি থাকে (১ - ১/২) = ১/২

১/২ কাজ ৮ দিনে করে ১০ জন
১/২ কাজ ১ দিনে করে (১০ × ৮) জন
১/২ কাজ ৪ দিনে করে ৮০/৪ = ২০ জন

∴ অতিরিক্ত লোক লাগবে = ২০ - ১০ জন = ১০ জন
৯৪৪.
A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?
  1. ক
    2 days
  2. খ
    3 days
  3. গ
    4 days
  4. ঘ
    5 days
  5. ঙ
    1 day
সঠিক উত্তর: ঘ
5 days
উত্তর
সঠিক উত্তর: ঘ
5 days
ঘ
ব্যাখ্যা
Question: A can do a piece of work in 12 days. B can do this work in 16 days. A started the work alone. After how many days should B join him, so that the work is finished in 9 days?

Solution:
A's work in 9 days = 9/12 = 3/4.
Remaining work = 1 - 3/4 = 1/4.

B can do full work in 16 days
1/4 portion of work was done by B in (1/4) × 16 = 4 days.
∴ B would have joined A after 9 - 4 = 5 days.
৯৪৫.
A and B can do a piece of work in 9 days, B and C in 12 days, A and C in 18 days. If all of them work together, then how much time will they take to finish the same work?
  1. ক
    6
  2. খ
    8
  3. গ
    7
  4. ঘ
    10
সঠিক উত্তর: খ
8
উত্তর
সঠিক উত্তর: খ
8
খ
ব্যাখ্যা
Question: A and B can do a work in 9 days, B and C can do it in 12 days and A and C can do it in 18 days. If all of them work together, in how many days they can finish the work?

Solution:
A + B can do in 1 day = 1/9 part
B + C can do in 1 day = 1/12 part
A + C can do in 1 day = 1/18 part 
2(A + B + C ) can do in 1 day = ((1/9) + (1/12) + (1/18)) = 1/4 part
∴ A + B + C can do in 1 day = 1/(4 × 2) part = 1/8 part 

∴ Total days needed = 1/(1/8) = 8 days
৯৪৬.
Sumi can type 10 pages in 5 minutes. Maria can type 5 pages in. 10 minutes. Working together, how many pages can they type in 30 minutes?
  1. ক
    70 pages
  2. খ
    75 pages
  3. গ
    78 pages
  4. ঘ
    80 pages
সঠিক উত্তর: খ
75 pages
উত্তর
সঠিক উত্তর: খ
75 pages
খ
ব্যাখ্যা
Question: Sumi can type 10 pages in 5 minutes. Maria can type 5 pages in. 10 minutes. Working together, how many pages can they type in 30 minutes?

Solution:
Sumi can type in 1 min = 10/5 = 2 pages 
Maria 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
৯৪৭.
A and B can do a work a piece of work in 12 days, B and C in 10 days and C and A in 6 days. How long would B take to do the same work alone?
  1. ক
    ক) 40 days
  2. খ
    খ) 48 days
  3. গ
    গ) 60 days
  4. ঘ
    ঘ) 120 days
সঠিক উত্তর: ঘ
ঘ) 120 days
উত্তর
সঠিক উত্তর: ঘ
ঘ) 120 days
ঘ
ব্যাখ্যা
(A + B)'s 1 day's work=1/12
(B + C)'s 1 day's work=1/10
(A + C)'s 1 day's work=1/6

[ (A + B)'s 1 day's work + (B + C)'s 1 day's work ] - (A + C)'s 1 day's work
= (1/12) + (1/10) - (1/6)
= (5 + 6 - 10)/60
⇒2(B's 1 day's work)=1/60
⇒B's 1 day's work=1/120

Hence, B alone can do the work in 120 days.
৯৪৮.
If 40 men can make 30 boxes in 20 days. How many more men are needed to make 60 boxes in 25 days?
  1. ক
    ক) 21
  2. খ
    খ) 24
  3. গ
    গ) 25
  4. ঘ
    ঘ) 27
সঠিক উত্তর: খ
খ) 24
উত্তর
সঠিক উত্তর: খ
খ) 24
খ
ব্যাখ্যা
M1 = 40 Men , D1 = 20 days , W1 = 30 Boxes
M2 = 40 + M , D2 = 25 days , W2 = 60 Boxes


৯৪৯.
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
    Tk. 30
  2. খ
    Tk. 35
  3. গ
    Tk. 40
  4. ঘ
    Tk. 42
সঠিক উত্তর: গ
Tk. 40
উত্তর
সঠিক উত্তর: গ
Tk. 40
গ
ব্যাখ্যা
Question: 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?

Solution: 
Man's wage = 3 boy's wage
Daily wages for them = 800/5
 = 160

A man and a boy = 4 boys 
4 boys' wage  = 160
4 boys' wag = 160
⇒ boy's wage = Tk. 40
৯৫০.
20 men complete one-third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?
  1. ক
    ক) 32
  2. খ
    খ) 21
  3. গ
    গ) 24
  4. ঘ
    ঘ) 12
সঠিক উত্তর: ঘ
ঘ) 12
উত্তর
সঠিক উত্তর: ঘ
ঘ) 12
ঘ
ব্যাখ্যা
Let the total number of men be x
Work done = 1/3
Remaining work = (1 - 1/3) = 2/3
More work, More men (Direct proportion)
More days, Less men (Indirect proportion)
Work 1/3 : 2/3
Days 25 : 20
1/3 × 25 × x = 2/3 × 20 × 20
x = 32
∴ More men to be employed = (32 - 20) = 12
৯৫১.
A rope makes 70 rounds of the circumference of a cylinder whose radius of the base is 14 cm. How many times can it go round a cylinder with radius 20 cm?
  1. ক
    ক) 39
  2. খ
    খ) 49
  3. গ
    গ) 59
  4. ঘ
    ঘ) 69
সঠিক উত্তর: খ
খ) 49
উত্তর
সঠিক উত্তর: খ
খ) 49
খ
ব্যাখ্যা

Let the required number of rounds be x
More radius, Less rounds (Indirect proportion)
∴ 20:14::70:x
⇔(20×x)=(14×70)
⇔ x= (14×70)/ 20
⇔ x=49

৯৫২.
A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?
  1. ক
    20 days
  2. খ
    22 days
  3. গ
    22.5 days
  4. ঘ
    25 days
সঠিক উত্তর: ঘ
25 days
উত্তর
সঠিক উত্তর: ঘ
25 days
ঘ
ব্যাখ্যা
Question: A can finish the job at the same time in which B and C together do it. If A and B together can finish the work in 10 days and C alone can do the work in 50 days, how many days B will take to complete the same job?

Solution:
The efficiency of A = B + C
(A + B) can finish the work in 10 days,
and C can finish the work in 50 days.

Now,
A + B = 10 days
C = 50 days

Assume the total work = LCM of the given days
∴ LCM of days = LCM of (10 and 50) = 50
Let the total work = 50

C's one day work = 50/50 = 1
(A + B)'s one day work = 5
i.e., (A + B + C)'s one day work = 5 +1=6
i.e., A + A = 6
⇒ 2A = 6
Or, A's one day work efficiency = 3

A + B = 5,
i.e., 3 + B = 5
Or, B's one day efficiency = 2

Hence, B alone can work in 50/2 = 25 days
৯৫৩.
A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:
  1. ক
    ক) 12 minutes
  2. খ
    খ) 18 minutes
  3. গ
    গ) 24 minutes
  4. ঘ
    ঘ) 16 minutes
সঠিক উত্তর: ক
ক) 12 minutes
উত্তর
সঠিক উত্তর: ক
ক) 12 minutes
ক
ব্যাখ্যা
Question: A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

Solution:
Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken;
= 1/6 : 1/3 : 1 = 1 : 2 : 6

Hence, time taken by A = 72/6
 = 12 minutes.
৯৫৪.
If (2 + √x) > 2√x, which of the following must be true?
  1. ক
    x < 1
  2. খ
    x < 2
  3. গ
    x < 3
  4. ঘ
    x < 4
  5. ঙ
    none of these
সঠিক উত্তর: ঘ
x < 4
উত্তর
সঠিক উত্তর: ঘ
x < 4
ঘ
ব্যাখ্যা

Question: If (2 + √x) > 2√x, which of the following must be true?

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

৯৫৫.
Hassan completed 1/3 portion of a job in 8 days and left. Then Jashim was recruited and he worked for 5 days and left the job. Hassan again joined and completed the rest of the work in 12 days. How many days would Jashim require to complete the job alone?
  1. ক
    ক) 10 days
  2. খ
    খ) 24 days
  3. গ
    গ) 30 days
  4. ঘ
    ঘ) 36 days
  5. ঙ
    ঙ) None
সঠিক উত্তর: গ
গ) 30 days
উত্তর
সঠিক উত্তর: গ
গ) 30 days
গ
ব্যাখ্যা
হাসান ৮ দিনে করে ১/৩ অংশ
সে ১ দিনে করে ১/(৮x৩) = ১/২৪ অংশ
তাহলে ১২ দিনে করবে (১x১২)/২৪ = ১/২ অংশ।
অর্থাৎ, সে ২০ দিনে করে (১/৩)+(১/২) = ৫/৬ অংশ।
জসিম বাকি কাজ {১-(৫/৬))= ১/৬ অংশ করে ৫ দিনে
তাহলে পুরো কাজটি একা করতে জসিমের লাগবে (৫x৬)/১= ৩০ দিন।
৯৫৬.
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
  1. ক
    ক) 30 days
  2. খ
    খ) 35 days
  3. গ
    গ) 40 days
  4. ঘ
    ঘ) 45 days
সঠিক উত্তর: ক
ক) 30 days
উত্তর
সঠিক উত্তর: ক
ক) 30 days
ক
ব্যাখ্যা
Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let time taken by B to complete a work be ′x′ days.
Therefore, time taken by A to the work =x + 50%x =1.5x days

Now,
Work done by B in one days = 1/x units
Work done by A in one day = 2/3x units

Thus, according to the question,
⇒1/x + 2/3x = 1/18
⇒5/3x = 1 /18
∴x =5 × 18/3 = 30

Hence, time taken by B to complete the work is 30 days
৯৫৭.
A can run 22m while B runs 25m. In a kilometer race B beats A by -
  1. ক
    110m
  2. খ
    120m
  3. গ
    140m
  4. ঘ
    160m
সঠিক উত্তর: খ
120m
উত্তর
সঠিক উত্তর: খ
120m
খ
ব্যাখ্যা
Question: A can run 22m while B runs 25m. In a kilometre race B beats A by -

Solution: 
while B covers 25m, A covers 22m
∴ B covers 1000m, A covers = (22 × 1000)/25 = 880m

∴ B beats A by = 1000 - 880 = 120m
৯৫৮.
A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2nd and 3rd day respectively, how long will it take the task to be completed?
  1. ক
    15 days
  2. খ
    14 days
  3. গ
    12 days
  4. ঘ
    10 days
  5. ঙ
    None of these
সঠিক উত্তর: ঙ
None of these
উত্তর
সঠিক উত্তর: ঙ
None of these
ঙ
ব্যাখ্যা
Question: A, B and C working individually can complete a task in 30 days, 15 days and 10 days respectively. If A starts working alone and B and C helps A on every 2nd and 3rd day respectively, how long will it take the task to be completed?

Solution:
A একা ১ দিনে করে = ১/৩০ অংশ
B একা ১ দিনে করে = ১/১৫ অংশ
C একা ১ দিনে করে = ১/১০ অংশ

প্রথম ১০ দিনের জন্য হিসেব করে পাই,
প্রথম ১০ দিনে A কাজ করে ১০ দিন তথা = ১০/৩০ অংশ কাজ
প্রথম ১০ দিনে B কাজ করে ৫ দিন তথা = ৫/১৫ অংশ কাজ
প্রথম ১০ দিনে C কাজ করে ৩ দিন তথা = ৩/১০ অংশ কাজ
প্রথম ১০ দিনে A,B,C কাজ করে (১০/৩০) + (৫/১৫) + (৩/১০) = (১০ + ১০ + ৯)/৩০ = ২৯/৩০ অংশ
বাকি ১ - (২৯/৩০) = ১/৩০ অংশ কাজ করতে ১ দিন সময় লাগবে।

∴ মোট দিন = ১০ + ১ = ১১ দিন
৯৫৯.
If 12 workers can build a wall in 6 days, how long would it take 9 workers to build the same wall?
  1. ক
    4 days
  2. খ
    6 days
  3. গ
    8 days
  4. ঘ
    9 days
সঠিক উত্তর: গ
8 days
উত্তর
সঠিক উত্তর: গ
8 days
গ
ব্যাখ্যা

Question: If 12 workers can build a wall in 6 days, how long would it take 9 workers to build the same wall?

Solution:
12 workers can build a wall in 6 days.
∴ 1 worker would take = 6 × 12 days = 72 days.
∴ 9 workers would take = 72/9 days = 8 days.

৯৬০.
To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?
  1. ক
    36 days
  2. খ
    30 days
  3. গ
    40 days
  4. ঘ
    38 days
সঠিক উত্তর: ক
36 days
উত্তর
সঠিক উত্তর: ক
36 days
ক
ব্যাখ্যা

Question: To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?

Solution:
Let Y takes x days to complete the work
Then X will take 25% more i.e 125% of x days i.e 5/4x days.
So the one day work of X and Y together will be
(1/x) +{1/(5/4x)} = 1/20
⇒ (1/x) + (4/5x) = 1/20
⇒ 9/5x = 1/20
⇒ x = 36
∴ Y takes 36 days to complete the work.

৯৬১.
A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the remaining food lasts for 35 days, the number of men originally in the fort were -
  1. ক
    ক) 2500
  2. খ
    খ) 3000
  3. গ
    গ) 3500
  4. ঘ
    ঘ) 4000
সঠিক উত্তর: গ
গ) 3500
উত্তর
সঠিক উত্তর: গ
গ) 3500
গ
ব্যাখ্যা

Let, there be x men originally.
So, x men had provisions for 40 days whereas (x + 500) men consumed it in 35 days.
more men, Less days [Indirect proportion]
∴ (x + 500) : x = 40 : 35
⇒ 35(x+ 500) = 40x
⇒ 5x = 35 × 500
⇒ x = (35 × 500)/5
= 3500.

৯৬২.
Two pipes can fill an empty tank separately in 24 minutes and 40 minutes respectively and a third pipe can empty 30 gallons of water per minute. If all three pipes are open, empty tanks become full in one hour. The capacity of the tank (in gallons) is:
  1. ক
    ক) 350 gallons
  2. খ
    খ) 450 gallons
  3. গ
    গ) 500 gallons
  4. ঘ
    ঘ) 600 gallons
সঠিক উত্তর: ঘ
ঘ) 600 gallons
উত্তর
সঠিক উত্তর: ঘ
ঘ) 600 gallons
ঘ
ব্যাখ্যা
Let capacity of the tank = x gallons;
Part of the tank filled in 1 minute = x/24 + x/40 - 30
x/24 + x/40 - 30 = x/60
x = 600 gallons
৯৬৩.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 9
সঠিক উত্তর: গ
গ) 12
উত্তর
সঠিক উত্তর: গ
গ) 12
গ
ব্যাখ্যা

3 pumps in 2 days empties by working 8 hrs
1      ''         2  ''           ''             ''           ''   (8 × 3)  hrs
1      ''         1  ''           ''             ''           ''   (8 × 3 × 2)  hrs
∴ 4   ''         1  ''           ''             ''           ''   (8 × 3 × 2) /4 hrs
                                                                 = 12 hrs

৯৬৪.
A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for Tk. 75000. The share of B in the contracted money will be:
  1. ক
    ক) Tk. 40000
  2. খ
    খ) Tk. 45000
  3. গ
    গ) Tk. 35000
  4. ঘ
    ঘ) Tk. 30000
সঠিক উত্তর: খ
খ) Tk. 45000
উত্তর
সঠিক উত্তর: খ
খ) Tk. 45000
খ
ব্যাখ্যা
Question: A and B can complete a piece of work in 15 days and 10 days respectively. They got a contract to complete the work for Tk. 75000. The share of B in the contracted money will be:

Solution: 
Ratio of number of days taken by A and B to complete the work = 15 : 10 = 3 : 2
∴ Ratio of efficiency of A and B = 2 : 3

Let their share is in the ratio of 2x and 3x
Now,
2x + 3x = 75000
⇒ 5x = 75000
∴ x = 15000

∴ Share of B = 3x
= 15000 × 3
= 45000 Taka
৯৬৫.
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
  2. খ
    45
  3. গ
    48
  4. ঘ
    30
সঠিক উত্তর: গ
48
উত্তর
সঠিক উত্তর: গ
48
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

৯৬৬.
12 men complete a work in 9 days. After they have worked for 6 days 6 more men join them. How many days will they take to complete the remaining work? 
  1. ক
    ক) 2 days
  2. খ
    খ) 3 days
  3. গ
    গ) 4 days
  4. ঘ
    ঘ) 6 days
সঠিক উত্তর: ক
ক) 2 days
উত্তর
সঠিক উত্তর: ক
ক) 2 days
ক
ব্যাখ্যা
Question: 12 men complete a work in 9 days. After they have worked for 6 days 6 more men join them. How many days will they take to complete the remaining work? 

Solution:
12 men's 9 days work = 1
1 man's 1 day's work = 1/108
12 men's 6 day's work = (12 × 6)/108
                                     = 2/3

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

18 men's 1 day's work =18/108 = 1/6

1/6 work is done by them in 1 day 
1/3 work is done by them in 6/3 = 2 days 
৯৬৭.
Working 5 hours a day, A can complete a work in 9 days and working 9 hours a day, B can complete the same work in 10 days. Working 6 hours a day, they can jointly complete the work in- 
  1. ক
    5 days
  2. খ
    7 days
  3. গ
    8 days
  4. ঘ
    6 days
সঠিক উত্তর: ক
5 days
উত্তর
সঠিক উত্তর: ক
5 days
ক
ব্যাখ্যা
Question: Working 5 hours a day, A can complete a work in 9 days and working 9 hours a day, B can complete the same work in 10 days. Working 6 hours a day, they can jointly complete the work in - 

Solution: 
Working 5 hours a day, for 9 days, A can finish the work in = (5 × 9) = 45 hours
Working 9 hours a day, for 10 days, B can finish the work in = (9 × 10) = 90 hours

both together can do in one hour = 1/45 + 1/90
= (2 + 1)/90
= 3/90
= 1/30

so, it will take them 30 hours to do the work.

hence, working 6 hours a day, they need = 30/6 = 5 days

So they will complete the work in 5 days working 6 hours each day.
৯৬৮.
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
    12 days
  2. খ
    15 days
  3. গ
    16 days
  4. ঘ
    18 days
সঠিক উত্তর: খ
15 days
উত্তর
সঠিক উত্তর: 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.

∴ The whole work is done in (3 × 5)
= 15 days.

৯৬৯.
Courier charges for packages to a certain destination are Tk. 65 for the first 250 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. 155?
  1. ক
    1155 gms
  2. খ
    1145gms
  3. গ
    1040 gms
  4. ঘ
    1150 gms
সঠিক উত্তর: ঘ
1150 gms
উত্তর
সঠিক উত্তর: ঘ
1150 gms
ঘ
ব্যাখ্যা
Question: Courier charges for packages to a certain destination are Tk. 65 for the first 250 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. 155?

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

ATQ,
65 + 10x = 155
⇒ 10x = 90
∴ x = 9

∴ The additional weight 100 × 9 = 100 × 9 = 900 grams
∴ Total weight will be 900 + 250 = 1150 gms
৯৭০.
A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days, With the help of C, they did the job in 4 days only. Then C alone can do the  job in:
  1. ক
    42/5 days
  2. খ
    48/5 days  
  3. গ
    43/5 days
  4. ঘ
    45 days 
সঠিক উত্তর: খ
48/5 days  
উত্তর
সঠিক উত্তর: খ
48/5 days  
খ
ব্যাখ্যা
Question: A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days, With the help of C, they did the job in 4 days only. Then C alone can do the  job in:

Solution: 
A একদিনে করে ১/১৬ অংশ 
B একদিনে করে ১/১২ অংশ 

C একদিনে করে (১/৪) - {(১/১২) + (১/১৬)}
= (১/৪) - (৭/৪৮)
= ৫/৪৮ 

C এর কাজটি করতে সময় লাগবে = ৪৮/৫ দিন
৯৭১.
A monkey climbs a 60m high pole. In first minute he climbs 6m and slips down 3m in the next minute. How much time is required by it to reach the top? 
  1. ক
    ক) 35 minutes
  2. খ
    খ) 33 minutes
  3. গ
    গ) 37 minutes
  4. ঘ
    ঘ) 40 minutes
সঠিক উত্তর: গ
গ) 37 minutes
উত্তর
সঠিক উত্তর: গ
গ) 37 minutes
গ
ব্যাখ্যা
শেষের মিনিটে সে slip করবে না, অর্থাৎ 54 মিটার উঠার পর 6 মিটার উঠে গেলে সে আর নিচে নামবে না।
তাই এখন দেখি এই 54 মিটার সে কত মিনিটে উঠে।
প্রতি 2 মিনিটে বানরটি উঠে = 6 - 3 = 3 মিটার।
অর্থাৎ 3 মিটার উঠে = 2 মিনিটে
∴ 54 মিটার উঠে = (2 × 54)/3
= 36 মিনিটে 
∴ খুঁটি বেয়ে উঠতে সময় লাগবে = 36 + 1 = 37 মিনিট
৯৭২.
A can do a work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?
  1. ক
    ক) 12 hours
  2. খ
    খ) 10 hours
  3. গ
    গ) 8 hours
  4. ঘ
    ঘ) 6 hours
সঠিক উত্তর: ক
ক) 12 hours
উত্তর
সঠিক উত্তর: ক
ক) 12 hours
ক
ব্যাখ্যা
Question: A can do a work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B take alone to do it? 

Solution: 
A's 1 hour work = 1/4
(B + C)'s 1 hour work = 1/3
(A + C)'s 1 hour work = 1/2

(A + B + C)'s 1 hour work = 1/4 + 1/3 = 7/12

∴ B's 1 hour work is = {(A + B + C)'s 1 hour work} - {(A + C)'s 1 hour work}
= 7/12 - 1/2
= 1/12

so, B alone can do it in 12 hours.
৯৭৩.
Akash are 5 times as efficient as Biplob. Akash can finish the work 60 days earlier than Biplob. If they work individually, how many days would they take to finish the work?
  1. ক
    ক) Akash = 10 days; Biplob = 50 days
  2. খ
    খ) Akash = 15 days; Biplob = 75 days
  3. গ
    গ) Akash = 20 days; Biplob = 80 days
  4. ঘ
    ঘ) Akash = 20 days; Biplob = 100 days
সঠিক উত্তর: খ
খ) Akash = 15 days; Biplob = 75 days
উত্তর
সঠিক উত্তর: খ
খ) Akash = 15 days; Biplob = 75 days
খ
ব্যাখ্যা

We know,
Speed of Work / Efficiency ∝ 1/Time needed
So more the efficiency, less time is needed to do the task.

Let us denote Akash by 'A' and Biplob by 'B'
Hence,
if A is 5 times faster than B, then B needs 5 times more time than A.
Let A need 'n' days to complete the work.
So B will need 5n days.
Also, 5n – n = 60 ------------------- Given
∴ n = 15 days = Days needed by A to complete work individually
Days needed by B to complete work individually = 5n = 5 x 15 = 75 days.

৯৭৪.
এক ব্যক্তি ৬০ ঘণ্টায় একটি নির্দিষ্ট দূরত্ব অতিক্রম করেন। যাত্রাপথের এক তৃতীয়াংশ দূরত্ব তিনি ৩০ কি.মি./ঘণ্টা এবং বাকী দুই তৃতীয়াংশ দূরত্ব ৪০ কি.মি./ঘণ্টা গতিতে চলেন। মোট দূরত্ব কত ছিল?
  1. ক
    ২০০০ কি.মি.
  2. খ
    ২১৬০ কি.মি.
  3. গ
    ২২২০ কি.মি.
  4. ঘ
    ২২৪৮ কি.মি.
  5. ঙ
    ২৪০০ কি.মি.
সঠিক উত্তর: খ
২১৬০ কি.মি.
উত্তর
সঠিক উত্তর: খ
২১৬০ কি.মি.
খ
ব্যাখ্যা
প্রশ্ন: এক ব্যক্তি ৬০ ঘণ্টায় একটি নির্দিষ্ট দূরত্ব অতিক্রম করেন। যাত্রাপথের এক তৃতীয়াংশ দূরত্ব তিনি ৩০ কি.মি./ঘণ্টা এবং বাকী দুই তৃতীয়াংশ দূরত্ব ৪০ কি.মি./ঘণ্টা গতিতে চলেন। মোট দূরত্ব কত ছিল?

সমাধান:
ধরি,
দূরত্ব = ক কি.মি.
ব্যক্তিটি ৬০ ঘণ্টায় ক দূরত্ব অতিক্রম করেন।
যাত্রাপথের এক তৃতীয়াংশ দূরত্ব অতিক্রম করতে সময় লাগে = (ক/৩)/৩০
= ক/৯০ ঘণ্টা

যাত্রাপথের বাকি অর্ধেক দূরত্ব অতিক্রম করতে সময় লাগে = (২ক/৩)/৪০
= ২ক/১২০ ঘণ্টা
= ক/৬০

প্রশ্নমতে,
(ক/৯০) + (ক/৬০) = ৬০
⇒ (২ক + ৩ক)/১৮০ = ৬০
⇒ ৫ক = ৬০ × ১৮০
⇒ ক = ১০৮০০/৫
∴ ক = ২১৬০ কি.মি.
৯৭৫.
A contractor employed 30 men to do a piece of work in 38 days. After 25 days, he employed 5 men more and the work was finished one day earlier. How many days he would have been behind, if he had not employed additional men?
  1. ক
    3
  2. খ
    1
  3. গ
    3/2
  4. ঘ
    2
সঠিক উত্তর: খ
1
উত্তর
সঠিক উত্তর: খ
1
খ
ব্যাখ্যা
Question: A contractor employed 30 men to do a piece of work in 38 days. After 25 days, he employed 5 men more and the work was finished one day earlier. How many days he would have been behind, if he had not employed additional men?

Solution:
Remaining days = 38 - 25 = 13,
Total 30 + 5 = 35 men work for (13 - 1) = 12 days.

Now,
35 men can complete the work in 12 days
∴ 1 men can complete the work in (12 × 35) days
∴ 30 men can complete the work in (12 × 35)/30 days
= 14 days

So, if additional men not added then he will be behind = 14 - 13) = 1 day.
৯৭৬.
A pump remover's water at a rate of 6 gallons per minute. How many hours will it take to remove 1800 gallons?
  1. ক
    ক) 4 hours
  2. খ
    খ) 5 hours
  3. গ
    গ) 3 hours
  4. ঘ
    ঘ) 6 hours
  5. ঙ
    ঙ) (11/2) hours
সঠিক উত্তর: খ
খ) 5 hours
উত্তর
সঠিক উত্তর: খ
খ) 5 hours
খ
ব্যাখ্যা
Question: A pump remover's 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
৯৭৭.
If A and B can complete a work together in 10 days, B and C together in 15 days, and A and C together in 12 days, then in how many days can B alone complete the work?
  1. ক
    24 days
  2. খ
    48 days
  3. গ
    54 days
  4. ঘ
    36 days
সঠিক উত্তর: ক
24 days
উত্তর
সঠিক উত্তর: ক
24 days
ক
ব্যাখ্যা
Question: If A and B can complete a work together in 10 days, B and C together in 15 days, and A and C together in 12 days, then in how many days can B alone complete the work?

Solution:
মনে করি,
সম্পূর্ণ কাজ = 1 অংশ

∴ (A + B) একদিনে করে = 1/10 অংশ। ..........(1)
(B + C) একদিনে করে = 1/15 অংশ। ..........(2)
(A + C) একদিনে করে = 1/12 অংশ। ..........(3)

(1), (2), (3) যোগ করে পাই,
2 × (A + B + C) = (1/10) + (1/15) + (1/12)
⇒ 2 × (A + B + C) = (6 + 4 + 5)/60 = 15/60
⇒ 2 × (A + B + C) = 1/4
⇒ (A + B + C) = 1/8

∴ A, B এবং C একসাথে একদিনে করে = 1/8 অংশ।

(A + B + C) একসাথে একদিনে করে 1/8 অংশ।
(A + C) একসাথে একদিনে করে 1/12 অংশ।

∴ B-এর একদিনের কাজ = 1/8 - 1/12
= (3 - 2)/24
= 1/24

অর্থাৎ,
B সম্পূর্ণ কাজ করে = (1 ÷ 1/24) = 24 দিনে
৯৭৮.
A man walks 10m east but runs 5m west every day. How many days will it take him to cross a building 380m east?
  1. ক
    ক) 75 days
  2. খ
    খ) 76 days
  3. গ
    গ) 78 days
  4. ঘ
    ঘ) 80 days
সঠিক উত্তর: ক
ক) 75 days
উত্তর
সঠিক উত্তর: ক
ক) 75 days
ক
ব্যাখ্যা

So, the man crosses (10 - 5) = 5 meters east everyday
As he will cross the 380th meter when for the last time he goes 10 m east, remaining distance will take (380 - 10)/5 = 74 days
Total 75 days will take to cross the building which is 380 m east.

৯৭৯.
M works twice as fast as N. If N can complete a work in 12 days immediately, the number of days in which M and N can together finish the work- 
  1. ক
    4 days
  2. খ
    6 days
  3. গ
    8 days
  4. ঘ
    2 days
সঠিক উত্তর: ক
4 days
উত্তর
সঠিক উত্তর: ক
4 days
ক
ব্যাখ্যা
Question: M works twice as fast as N. If N can complete a work in 12 days immediately, the number of days in which M and N can together finish the work- 

Solution:
N can complete a work in 12 days
So, M can complete the work in 6 days  

(M + N)'s 1 days work = (1/6 + 1/12) = 1/4 part
So, (M + N) can complete the work in 4 days.
৯৮০.
20 men can do a piece of work in 16 days. They worked together for 3 days, then 6 men joined. In how many days is the remaining work completed?
  1. ক
    18 days
  2. খ
    10 days
  3. গ
    20 days
  4. ঘ
    30 days
  5. ঙ
    36 days
সঠিক উত্তর: খ
10 days
উত্তর
সঠিক উত্তর: খ
10 days
খ
ব্যাখ্যা

Question: 20 men can do a piece of work in 16 days. They worked together for 3 days, then 6 men joined. In how many days is the remaining work completed?

Solution:
20 men can complete the work in 16 days.
So, total work = 16 × 20 = 320

∴ Work done by 20 men in 3 days = 20 × 3 = 60

∴ Remaining work = 320 - 60 = 260

After joining 6 men total men = 20 + 6 = 26

So, Time required to finish the remaining work = 260/26=10 days

৯৮১.
A man can do a piece of work in 60 hours. If he takes his son with him and both work together then the work is finished in 40 hours. How many hours will the son take to do the same job, if he worked alone on the job?
  1. ক
    20
  2. খ
    60
  3. গ
    100
  4. ঘ
    120
সঠিক উত্তর: ঘ
120
উত্তর
সঠিক উত্তর: ঘ
120
ঘ
ব্যাখ্যা
Question: A man can do a piece of work in 60 hours. If he takes his son with him and both work together then the work is finished in 40 hours. How many hours will the son take to do the same job, if he worked alone on the job?

Solution:
If the man takes 60 hours to complete the work, then he will finish (1/60)th of the work in 1 hour.
Let us assume that his son takes x hours to finish the same work.
If they work together for 1 hour they will finish 1/60 + 1/x = 1/40 of the work.
⇒ 1/x = 1/40 - 1/60
⇒ 1/x = (3 - 2)/120
⇒ 1/x = 1/120
∴ x = 120

The son, working alone would take 120 hours to complete the work.
৯৮২.
3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?
  1. ক
    ক) 8
  2. খ
    খ) 10
  3. গ
    গ) 12
  4. ঘ
    ঘ) 15
সঠিক উত্তর: গ
গ) 12
উত্তর
সঠিক উত্তর: গ
গ) 12
গ
ব্যাখ্যা
Let the required number of working hours per day be x.
More pumps, Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)
Pumps 4 : 3
                     ⟩ : : 8 : x
Days    1 : 2
4 × 1 × x = 3 × 2 × 8
x = 12
---------------------------------------
Shortly:
Pumps 4 : 3 and Days    1 : 2
by combining, we get, 
4 × 1 × x = 3 × 2 × 8
x = 12
৯৮৩.
If a light flashes every 6 seconds, how many times will it flash in 3/4 of an hour?
  1. ক
    ক) 450 times
  2. খ
    খ) 449 times
  3. গ
    গ) 451 times
  4. ঘ
    ঘ) 550 times
  5. ঙ
    ঙ) 448 times
সঠিক উত্তর: গ
গ) 451 times
উত্তর
সঠিক উত্তর: গ
গ) 451 times
গ
ব্যাখ্যা
Question: If a light flashes every 6 seconds, how many times will it flash in 3/4 of an hour?

Solution:
3/4 of an hour = (3/4) × 3600 seconds
= 2700 seconds

Now,
2700/6 = 450 times

The count start after the first flash. So, the light will flashes 450 + 1 = 451 times
৯৮৪.
A can do a work in 20 days, and B in 30 days. They work together for 6 days. How much of the work is left?
  1. ক
    1/3
  2. খ
    1/4
  3. গ
    1/2
  4. ঘ
    2/5
সঠিক উত্তর: গ
1/2
উত্তর
সঠিক উত্তর: গ
1/2
গ
ব্যাখ্যা

Question: A can do a work in 20 days, and B in 30 days. They work together for 6 days. How much of the work is left?

Solution:
A 20 দিনে করতে পারে কাজটির 1 অংশ
A 1 দিনে করতে পারে কাজটির 1/20 অংশ

B 30 দিনে করতে পারে কাজটির 1 অংশ
B 1 দিনে করতে পারে কাজটির 1/30 অংশ

A ও B 1 দিনে করতে পারে কাজটির (1/20) + (1/30) অংশ
= (3 + 2)/60 অংশ
= 5/60 অংশ
= 1/12 অংশ

A ও B 6 দিনে করতে পারে কাজটির 6/12 অংশ
= 1/2 অংশ

কাজ বাকি থাকে = 1 - 1/2 অংশ
= (2 - 1)/2 অংশ
= 1/2 অংশ

৯৮৫.
P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?
  1. ক
    6
  2. খ
    4
  3. গ
    5
  4. ঘ
    8
সঠিক উত্তর: ক
6
উত্তর
সঠিক উত্তর: ক
6
ক
ব্যাখ্যা

Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15
= 2/3
Remaining work = 1 - 2/3
= 1/3
Number of days in which P can finish the remaining work = (1/3)/(1/18)
= 6.

৯৮৬.
If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-
  1. ক
    18 days
  2. খ
    24 days
  3. গ
    25 days
  4. ঘ
    15 days
  5. ঙ
    None of these
সঠিক উত্তর: খ
24 days
উত্তর
সঠিক উত্তর: খ
24 days
খ
ব্যাখ্যা
Question: If A and B together can complete a work in 18 days, A and C together in 12 days, and B and C together in 9 days, then B alone can do the work in-

Solution:
One day's work of,
(A + B) = 1/18.......(1)
One day's work of,
(A + C) = 1/12.......(2)
One day's work of,
(B + C) = 19.......(3)

Adding(1),(2)and(3),
⇒ 2 × (A + B + C) = 1/18 + (1/12) + (1/9)
⇒ 2 (A + B + C) = 1/4
⇒ (A + B + C) = 1/8
Now,
⇒ B = (1/8) - (A + C)
⇒ B= (1/8) - (1/12)
One day's work of B = (3 - 2)/24 = 1/24
∴ B need 24 days
৯৮৭.
If 60 tk. is the cost for a quarter kg of potatoes, how much will 200 grams cost?
  1. ক
    48 tk.
  2. খ
    54 tk.
  3. গ
    66 tk.
  4. ঘ
    88 tk.
সঠিক উত্তর: ক
48 tk.
উত্তর
সঠিক উত্তর: ক
48 tk.
ক
ব্যাখ্যা
Question: If 60 tk. is the cost for a quarter kg of potatoes, how much will 200 grams cost?

Solution:
Let the required weight be x kg.

Less weight, Less cost (Direct Proportion)

250 : 200 : : 60 : x
⇒ 250/200 = 60/x
⇒ 250x = (200 × 60)
⇒ x = (200 × 60)/250
∴ x = 48
৯৮৮.
A boy read 3/8th of a book on one day and 4/5th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain?
  1. ক
    240
  2. খ
    300
  3. গ
    600
  4. ঘ
    800
সঠিক উত্তর: ক
240
উত্তর
সঠিক উত্তর: ক
240
ক
ব্যাখ্যা
Question: A boy read 3/8th of a book on one day and 4/5th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain?

Solution:
ধরি, বইয়ে মোট পৃষ্ঠা আছে = x টি
১ম দিনে পড়ে = 3x/8 অংশ
বাকি থাকে = x - (3x/8) = 5x/8 অংশ

২য় দিনে পড়ে = (5x/8) এর 4/5 অংশ
= x/2 অংশ

মোট পড়া হয়েছে = 3x/8 + x/2 = (3x + 4x)/8 = 7x/8

প্রশ্নমতে,
x - (7x/8) = 30
⇒ x/8 = 30
⇒ x = 30 × 8
∴ x = 240

মোট পৃষ্ঠা সংখ্যা 240
৯৮৯.
Aman is 20% more efficient than Atique. Atique alone can build a craft in 30 days. Find the number of days taken by Aman to finish the same piece of work?
  1. ক
    ক) 16 days
  2. খ
    খ) 21 days
  3. গ
    গ) 25 days
  4. ঘ
    ঘ) 27 days
সঠিক উত্তর: গ
গ) 25 days
উত্তর
সঠিক উত্তর: গ
গ) 25 days
গ
ব্যাখ্যা
The ratio of times taken by Aman and Atique
= 120 : 100
= 6: 5
Suppose Aman takes x days to do the work.
6 : 5 = 30 : x
or, 6x = 150
     x = 25 days
৯৯০.
Eight printers working together can print 960 documents in 6 days. If 3 printers stop working, how many documents can the remaining printers print in 9 days?
  1. ক
    900 documents
  2. খ
    1200 documents
  3. গ
    1000 documents
  4. ঘ
    1500 documents
সঠিক উত্তর: ক
900 documents
উত্তর
সঠিক উত্তর: ক
900 documents
ক
ব্যাখ্যা

Question: Eight printers working together can print 960 documents in 6 days. If 3 printers stop working, how many documents can the remaining printers print in 9 days?

Solution:
8টি প্রিন্টার 6 দিনে প্রিন্ট করে = 960টি ডকুমেন্ট
∴ 1টি প্রিন্টার 6 দিনে প্রিন্ট করে = 960/8 = 120টি ডকুমেন্ট
∴ 1টি প্রিন্টার 1 দিনে প্রিন্ট করে = 120/6 = 20টি ডকুমেন্ট

অবশিষ্ট প্রিন্টার = 8 - 3 = 5টি

∴ 5টি প্রিন্টার 9 দিনে প্রিন্ট করবে = 20 × 5 × 9 = 900টি ডকুমেন্ট

৯৯১.
15 workers can build 45 chairs working 6 hours per day. How many extra workers are required to produce 60 chairs working 4 hours per day?
  1. ক
    0 workers
  2. খ
    10 workers
  3. গ
    12 workers
  4. ঘ
    15 workers
সঠিক উত্তর: ঘ
15 workers
উত্তর
সঠিক উত্তর: ঘ
15 workers
ঘ
ব্যাখ্যা

Question: 15 workers can build 45 chairs working 6 hours per day. How many extra workers are required to produce 60 chairs working 4 hours per day?

Solution:
6 ঘণ্টা কাজ করে 45টি চেয়ার তৈরি করে 15 জন শ্রমিক 
1 ঘণ্টা কাজ করে 1টি চেয়ার তৈরি করে = (15 × 6) /45 জন শ্রমিক 
4 ঘণ্টা কাজ করে 60টি চেয়ার তৈরি করে = (15 × 6 × 60)/(45 × 4) জন শ্রমিক 
= 30 জন

∴ অতিরিক্ত শ্রমিকের সংখ্যা = 30 - 15 = 15 জন

৯৯২.
A garrison has food for 40 days for 200 soldiers. After 10 days, 50 soldiers leave. How many more days will the remaining food last?
  1. ক
    20 days
  2. খ
    30 days
  3. গ
    35 days
  4. ঘ
    40 days
সঠিক উত্তর: ঘ
40 days
উত্তর
সঠিক উত্তর: ঘ
40 days
ঘ
ব্যাখ্যা

Question: A garrison has food for 40 days for 200 soldiers. After 10 days, 50 soldiers leave. How many more days will the remaining food last?

Solution:
দেওয়া আছে,
40 দিনের খাদ্য আছে = 200 জনের

10 দিন পর 50 জন সৈন্য চলে গেলে,
 বাকি দিন = 40 - 10 = 30 দিন
বাকি সৈন্য = 200 - 50 = 150 জন

বাকি খাদ্যে,
200 জন সৈন্যের চলবে = 30 দিন
∴ 1 জন সৈন্যের চলবে =30 × 200 দিন 
∴ 150 জন সৈন্যের চলবে = (30 × 200)/150 = 40 দিন 

সুতরাং বাকি খাদ্যে 40 দিন চলবে।

৯৯৩.
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
    4
  2. খ
    5
  3. গ
    6
  4. ঘ
    7
সঠিক উত্তর: গ
6
উত্তর
সঠিক উত্তর: গ
6
গ
ব্যাখ্যা
Question: 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?

Solution:
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
৯৯৪.
If 5 men can colour 50-meter long cloth in 5 days, in many days 4 men can color a 40-meter long cloth?
  1. ক
    5 days
  2. খ
    6 days
  3. গ
    4 days
  4. ঘ
    3 days
সঠিক উত্তর: ক
5 days
উত্তর
সঠিক উত্তর: ক
5 days
ক
ব্যাখ্যা
Question: If 5 men can colour 50-meter long cloth in 5 days, in many days 4 men can color a 40-meter long cloth?

Solution:
M1D1W2 = M2D2W1
⇒ 5 × 5 × 40 = 4 × D2 × 50
⇒ D2 = (5 × 5 × 40)/(4 × 50)
∴ D2 = 5
৯৯৫.
Six identical machines can produce 540 articles in 12 hours. How many articles would 8 such machines produce in 15 hours? 
  1. ক
    700 articles
  2. খ
    900 articles
  3. গ
    800 articles
  4. ঘ
    500 articles
সঠিক উত্তর: খ
900 articles
উত্তর
সঠিক উত্তর: খ
900 articles
খ
ব্যাখ্যা

Question: Six identical machines can produce 540 articles in 12 hours. How many articles would 8 such machines produce in 15 hours?

Solution: 
Total articles produced by 6 machines in 12 hours = 540.
Articles produced by 1 machine in 12 hours = 540/6
Articles produced by 1 machine in 1 hour = 540/(6×12) = 7.5 articles

So, Articles produced by 8 machines in 15 hours = 7.5 × 8 × 15 
= 900 articles

৯৯৬.
A student loses 1 mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 100 questions in an exam and scores 68 marks, how many of them were correct?
  1. ক
    50
  2. খ
    56
  3. গ
    58
  4. ঘ
    60
সঠিক উত্তর: খ
56
উত্তর
সঠিক উত্তর: খ
56
খ
ব্যাখ্যা
Question: A student loses 1 mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 100 questions in an exam and scores 68 marks, how many of them were correct?

Solution:
ধরি,
মোট ভুল উত্তর = ক টি
প্রতিটি ভুল উত্তরের জন্য প্রকৃতপক্ষে কাঁটা যায় = (২ + ১) = ৩ নম্বর।

প্রশ্নমতে,
(২ × ১০০) - ৩ক = ৬৮
বা, ৩ক = ২০০ - ৬৮
বা, ৩ক = ১৩২
∴ ক = ৪৪

∴ সঠিক উত্তর = (১০০ - ৪৪) = ৫৬টি
৯৯৭.
A man completes a certain journey by a car. If he covered 40% of the distance at the speed of 20kmph. 30% of the distance at 15 kmph and the remaining of the distance at 30 kmph, his average speed is-
  1. ক
    15 kmph
  2. খ
    20 kmph
  3. গ
    25 kmph
  4. ঘ
    30 kmph
সঠিক উত্তর: খ
20 kmph
উত্তর
সঠিক উত্তর: খ
20 kmph
খ
ব্যাখ্যা
Question: A man completes a certain journey by a car. If he covered 40% of the distance at the speed of 20kmph. 30% of the distance at 15 kmph and the remaining of the distance at 30 kmph, his average speed is-

Solution:
Suppose, total distance = 100 km

He covered 40% of the distance at the speed of 20 kmph
His time taken = 40/20 = 2 hours

He covered 30% of the distance at 15 kmph
His time taken = 30/15 = 2 hours

He covered the remaining of the distance at 30 kmph
The remaining of the distance = 100% - (40 + 30)% = 30%
His time taken = 30/30 = 1 hour

∴ Average speed = Total distance/time
= 100/(2 + 2 + 1)
= 20 kmph
৯৯৮.
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many days men will be catered to with the remaining meal?
  1. ক
    ক) 20 men
  2. খ
    খ) 24 men
  3. গ
    গ) 30 men
  4. ঘ
    ঘ) 36 men
সঠিক উত্তর: গ
গ) 30 men
উত্তর
সঠিক উত্তর: গ
গ) 30 men
গ
ব্যাখ্যা
Question: In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many days men will be catered to with the 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
৯৯৯.
42 binders can bind 1400 books in 15 days. How many binders will be required. bind 800 books in 20 days?
  1. ক
    14 binders
  2. খ
    16 binders
  3. গ
    18 binders
  4. ঘ
    20 binders
সঠিক উত্তর: গ
18 binders
উত্তর
সঠিক উত্তর: গ
18 binders
গ
ব্যাখ্যা
Question: 42 binders can bind 1400 books in 15 days. How many binders will be required to bind 800 books in 20 days?

Solution:
In 15 days 1400 books can be bound by 42 binders
In 1 day 1 book can be bound by (42 × 15)/1400 binders
In 20 days 800 books can be bound by (42 × 15 × 800)/(1400 × 20) binders
= 18 binders
১,০০০.
In a 100 m race A runs at a speed of 1.66 m/s. If A gives a start of 4m to B and still beats him by 12 seconds. What is the speed of B?
  1. ক
    ক) 1.33 m/s
  2. খ
    খ) 2.66 m/s
  3. গ
    গ) 3 m/s
  4. ঘ
    ঘ) 4.25 m/s
সঠিক উত্তর: ক
ক) 1.33 m/s
উত্তর
সঠিক উত্তর: ক
ক) 1.33 m/s
ক
ব্যাখ্যা

Time is taken by A to cover 100 meters = 60 seconds
A gives a start of 4 seconds then time takes by B = 72 seconds
B takes 72 seconds to cover 96 meters
Speed of B = 96/72 = 1.33 m/s