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Test Level 2: Time & Work - 1 - CAT MCQ


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10 Questions MCQ Test - Test Level 2: Time & Work - 1

Test Level 2: Time & Work - 1 for CAT 2024 is part of CAT preparation. The Test Level 2: Time & Work - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Time & Work - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Time & Work - 1 below.
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Test Level 2: Time & Work - 1 - Question 1
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A and B work together for 8 days to complete a piece of work and B and C work together for 12 days to complete the same work. C alone can complete the work in 24 days and A is twice as efficient as B. How much time does it take to complete the work if all the three work together?  

Detailed Solution for Test Level 2: Time & Work - 1 - Question 1

1/A + 1/B = 1/8 ... (i)
1/B + 1/C = 1/12 ... (ii)
1/C = 1/24 ... (iii)
On solving, we get A = 12, B = 24 and C = 24
Therefore, 1/A + 1/B + 1/C = 1/6
All three together can complete the work in 6 days.

Test Level 2: Time & Work - 1 - Question 2
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A, B and C can do a piece of work in 20, 30 and 40 days, respectively. A and C started the work and B joined 4 days later. A left 8 days before the completion of work and C was also absent for 5 days in between. How many days will it take for the work to be completed?

Detailed Solution for Test Level 2: Time & Work - 1 - Question 2

Assume that it takes 'd' days for the work to be completed.
A works for (d - 8) days,
B works for (d - 4) days,
C works for (d - 5) days.

6d - 48 + 4d - 16 + 3d - 15 = 120
13d = 199
d =  days

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Test Level 2: Time & Work - 1 - Question 3
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A group of employees is working on a project. If 10 more employees join them, then the project will be completed in 2/3 of the time. If the work has to be completed in 1/3 of the time, then how many more employees have to join?

Detailed Solution for Test Level 2: Time & Work - 1 - Question 3

Let M be number of employees present initially and d be the number of days taken by M employees to complete the work.
Md = (M + 10) 2/3 d
Solving, M = 20 
To complete the work in 1/3 of the time, the number of employees should be 3 times (60).
So, 40 more employees have to join.

Test Level 2: Time & Work - 1 - Question 4
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A can do a piece of work in 20 days, working 8 hours a day and B can do the same work in 30 days, working 10 hours a day. If both A and B work together for 5 hours a day, how many days will they take to complete the same work?
Detailed Solution for Test Level 2: Time & Work - 1 - Question 4

A needs 160 hours and B needs 300 hours to complete the work individually.
So, time required by A and B together


Number of days required when A and B work 5 hours a day 

Test Level 2: Time & Work - 1 - Question 5
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A and B together can complete a piece of work in 25 days. B and C together can complete the same work in 30 days. How many days would A and C take to complete the work?  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 5

A and B can do 1/25 th of the work in 1 day.
B and C can do 1/30th of the work in 1 day.
From this, we cannot say anything about A and C.

Test Level 2: Time & Work - 1 - Question 6
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The amount of work done by a man on nth day after starting a piece of work is n times the amount of work that can be done on the first day. If 8 men start the work, it can be completed in 10 days. How many men should work if the work has to be completed in 4 days?  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 6

Let each of the 8 men do x units of work on the first day.
Total work done = 8(x + 2x + 3x + 4x + 5x + 6x + 7x + 8x + 9x + 10x) = 440x
To do the same 440x units work in 4 days, let n men be required.
So, n(x + 2x + 3x + 4x) = 440x
⇒ n = 44

Test Level 2: Time & Work - 1 - Question 7
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A man started a piece of work on the first day. The second day, one more person joined him. The next day, one more person joined. Everyday, one new person joined until the work got completed. If the work was completed in 15 days, how many days would 10 men take to complete the same work, given that they worked regularly and efficiency of all men is the same?  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 7

Let one day work of a man = x units
∵1st day = x
2nd day = 2x
……………..
……………
15th day = 15x
Total work done in 15 days = x + 2x + 3x + ... + 15x = 120x 
So, time taken to complete 120x work by 10 men is  120x/10x = 12 days

Test Level 2: Time & Work - 1 - Question 8
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If 300 men could do a piece of work in 16 days, then how many men would do 1/4 of the same work in 15 days?  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 8

300 men do 1 work in 16 days.
So, M1 = 300, D1 = 16, W1 = 1
Let y men do 1/4 work in 15 days.
Then, M2 = y, D2 = 15, W2 = 1/4
According to the formula:
M1D1W2 = M2D2W1
300 x 16 x (1/4) = y x 15 x 1

Test Level 2: Time & Work - 1 - Question 9
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A alone can finish a piece of work in 12 days and B alone can do it in 18 days. If they work together and finish it, then out of total wages of Rs. 50, A will get  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 9

A can finish the work in 12 days.
B can finish the work in 18 days.
∴ Ratio of their one-day work = 1/12 : 1/18 = 3 : 2
∴ If they work together and finish the work, they get the assigned amount in the ratio 3 : 2. That is, A will get Rs. 30 and B will get Rs. 20 (∵ total amount = Rs. 50).

Test Level 2: Time & Work - 1 - Question 10
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Two inlet pipes A and B can fill a tank in 24 hours and 30 hours, respectively. An outlet pipe C can empty the tank in 60 hours. The pipe C is continuously open and the pipes A and B work on alternate hours, starting with A. How much time does it take to fill the tank?  
Detailed Solution for Test Level 2: Time & Work - 1 - Question 10

In the first hour, A and C operate 

In the second hour, B and C operate 

Let V be the total volume of the tank. 
Time taken to fill 5/10th of the total volume of tank = 2 hours
Time taken to fill the total volume of the tank 

So, in 48 hours, the tank will be full.

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