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


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

Test Level 1: Time & Work - 2 for CAT 2024 is part of CAT preparation. The Test Level 1: Time & Work - 2 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Time & Work - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Time & Work - 2 below.
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Test Level 1: Time & Work - 2 - Question 1

P, Q and R are employed to do a piece of work for Rs. 529. P and R are supposed to finish 19/23 of the work together. How much shall be paid to Q?  

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

Work done by Q

Test Level 1: Time & Work - 2 - Question 2

It was expected that 10 men together would complete a piece of work in 40 days. But after a few days, they increased their efficiency by 25% and completed the work six days earlier. How many days after the start of the work did they increase their efficiency?  

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

Assume each man could do 'x' work in 1 day.
So, total work = 10 × 40x = 400x
But they completed the work in 34 days (40 - 6).
Assume after 'd' days, they increased their efficiency.
After increasing the efficiency, they could do 1.25x work in 1 day.
So, 400x = 10 × d × x + 10 (34 - d)1.25x.
⇒ 40 = d + (34 - d)1.25
⇒ 0.25d = 2.5  d = 10
Thus, they increased their efficiency 10 days after the start of the work.
Hence, answer option 4 is correct.

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Test Level 1: Time & Work - 2 - Question 3

A swimming pool is filled with water through four pipes, and there is an outlet pipe which can empty the pool in 30 minutes. The first pipe can fill the pool in 40 minutes; the second and third pipes can fill it in 15 minutes; the second and fourth pipes can fill it in 25 minutes; and the third and fourth pipes can fill it in 12 minutes.

In what time will the pool be filled if all the five pipes are working simultaneously?

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

Suppose the first pipe takes A minutes, the second pipe takes B minutes, the third pipe takes C minutes and the fourth pipe takes D minutes to fill the pool.

Add equations (ii), (iii) and (iv): 

The fifth pipe can empty the tank in 30 minutes.
So, combined time taken by all the five pipes

Test Level 1: Time & Work - 2 - Question 4

Raju can do 25% of a piece of work in 5 days. How many days will he take to complete the work ten times?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 4

He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.

Test Level 1: Time & Work - 2 - Question 5

A can do a piece of work in 20 days and B can do it in 15 days. How long will they take if both work together?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 5

A’s one day work will be 5%, while B will do 6.66 % of the work in one day. Hence, their total work will be 11.66% in a day.
In 8 days they will complete → 11.66 x 8 = 93.33%
This will leave 6.66% of the work. This will correspond to 4/7 of the ninth day since in 6.66/11.66 both the numerator and the denominator are divisible by 1.66.

Test Level 1: Time & Work - 2 - Question 6

Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In how many days can Archana do it alone?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 6

N + A = 10% 
N = 8.33% 
Hence A = 1.66% → 60 days.

Test Level 1: Time & Work - 2 - Question 7

4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 7

24 man days + 18 women days = 20 man days + 28 woman days
→ 4 man days = 10 woman days.
→ 1 man day = 2.5 woman days
Total work = 24 man days + 18 woman days = 60 woman days + 18 woman days = 78 woman days.
Hence, 1 man + 1 woman = 3.5 women can do it in 78/3.5 = 156/7 = 22(2/7) days.

Test Level 1: Time & Work - 2 - Question 8

A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will it take for C alone to finish the work?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 8

A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 days.

Test Level 1: Time & Work - 2 - Question 9

A and B undertake to do a piece of work for ₹ 100. A can do it in 5 days and B can do it in 10 days. With the help of C, they finish it in 2 days. How much should C be paid for his contribution?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 9

A = 20%, B = 10% and A + B + C = 50%. Hence, C = 20%. Thus, in two days, C contributes 40% of the total work and should be paid 40% of the total amount.

Test Level 1: Time & Work - 2 - Question 10

Arun and Vinay together can do a piece of work in 7 days. If Arun does twice as much work as Vinay in a given time, how long will Arun alone take to do the work.

Detailed Solution for Test Level 1: Time & Work - 2 - Question 10

Let the time taken by Arun be ‘t’ days. Then, time taken by Vinay = 2t days. 1/t + 1/2t = 1/7 → t = 10.5

Test Level 1: Time & Work - 2 - Question 11

X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 11

30X = 20 (X + 6) → 10X = 120 → X = 12.

Test Level 1: Time & Work - 2 - Question 12

Raju can do a piece of work in 10 days, Vicky in 12 days and Tinku in 15 days. They all start the work together, but Raju leaves after 2 days and Vicky leaves 3 days before the work is completed. In how many days is the work completed?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 12

Raju = 10%, Vicky = 8.33% and Tinku = 6.66%. Hence, total work for a day if all three work = 25%.
In 2 days they will complete, 50% work. On the third day onwards Raju doesn’t work. The rate of work will become 15%. Also, since Vicky leaves 3 days before the actual completion of the work, Tinku works alone for the last 3 days (and must have done the last 6.66 x 3 = 20% work alone). This would mean that Vicky leaves after 80% work is done. Thus, Vicky and Tinku must be doing 30% work together over two days.
Hence, total time required = 2 days (all three) + 2 

Test Level 1: Time & Work - 2 - Question 13

Manoj takes twice as much time as Anjay and thrice as much as Vijay to finish a piece of work. Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 13

Let Anjay take 3t days, Vijay take 2t days and Manoj take 6t days in order to complete the work. Then we get: 1/3t +
1/2t + 1/6t = 1 → t = 1. Thus, Manoj would take 6t = 6 days to complete the work.

Test Level 1: Time & Work - 2 - Question 14

Apurva can do a piece of work in 12 days. Apurva and Amit complete the work together and were paid ₹ 54 and ₹ 81 respectively. How many days must they have taken to complete the work together?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 14

Since the ratio of money given to Apurva and Amit is 2:3, their work done would also be in the same ratio. Thus, their time ratio would be 3:2 (inverse of 2:3). So, if Apurva takes 12 days, Amit would take 8 days and the total number of days required (t) would be given by the equation:
(1/12 + 1/8)t = 1 → t = 24/5 = 4.8 days

Test Level 1: Time & Work - 2 - Question 15

In a company XYZ Ltd. a certain number of engineers can develop a design in 40 days. If there were 5 more engineers, it could be finished in 10 days less. How many engineers were there in the beginning?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 15

40n = 30 (n + 5) → n = 15

Test Level 1: Time & Work - 2 - Question 16

A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many more days will B finish the work?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 16

A’s rate of working is 10 per cent per day while B’s rate of working is 5 per cent per day. In 5 days they will complete 75 per cent work. Thus the last 25 per cent would be done by B alone. Working at the rate of 5 per cent per day, B would do the work in 5 days.

Test Level 1: Time & Work - 2 - Question 17

Ajay and Vijay undertake to do a piece of work for ₹ 200. Ajay alone can do it in 24 days while Vijay alone can do it in 30 days. With the help of Pradeep, they finish the work in 12 days. How much should Pradeep get for his work?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 17

Ajay’s daily work = 4.1666%, Vijay’s daily work = 3.33% and the daily work of all the three together is 8.33%. Hence, Pradeep’s daily work will be 0.8333%. Hence, he will end up doing 10% of the total work in 12 days. This will mean that he will be paid ₹ 20.

Test Level 1: Time & Work - 2 - Question 18

Ajay, Vijay and Sanjay are employed to do a piece of work for ₹ 529. Ajay and Vijay together are supposed to do 19/23 of the work and Vijay and Sanjay together 8/23 of the work. How much should Ajay be paid?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 18

A + V + S = 1      (1) 
A + V = 19/23 
V + S = 8/23 
→ A + 2V + S = 27/23     (2) 
(2)–(1) gives us: V = 4/23.

Test Level 1: Time & Work - 2 - Question 19

In a fort there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 19

After 27 days, food left = 4 x 200 = 800 soldier days worth of food. Since, now there are only 80 soldiers, this food would last for 800/80 = 10 days.
Number of extra days for which the food lasts = 10 – 4 = 6 days.

Test Level 1: Time & Work - 2 - Question 20

Ajay and Vijay can do a piece of work in 28 days. With the help of Manoj, they can finish it in 21 days. How long will Manoj take to finish the work all alone?

Detailed Solution for Test Level 1: Time & Work - 2 - Question 20

Ajay + Vijay = 1/28 and Ajay + Vijay + Manoj = 1/21.
Hence, Manoj = 1/21 – 1/28 = 1/84.
Hence, Manoj will take 84 days to do the work.

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