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

Correct Answers :

[C]

Explanation :

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

2. 6 men can do a piece of work in 12 days. How many
men are needed to do the work in 18 days.

Correct Answers :

[C]

Explanation :

6 men for 12 days means 72 mandays. This would be equal to 4 men for 18 days.

3. *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?

Correct Answers :

[B]

Explanation :

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.

4. In Previous question if C, who can finish the same work in
25 days, joins them, then how long will they take to complete the work?

Correct Answers :

[A]

Explanation :

A’s work = 5% per day

B’s work = 6.66% per day

C’s work = 4% per day.

Total no. of days = 100/15.66 = 300/47 = 6(18/47)

5. 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?

Correct Answers :

[A]

Explanation :

N + A = 10%

N = 8.33%

Hence A = 1.66% → 60 days.

6. Baba alone can do a piece of work in 10 days. Anshu
alone can do it in 15 days. If the total wages for the work is ₹50. How much should Baba be paid
if they work together for the entire duration of the work?

Correct Answers :

[A]

Explanation :

The ratio of the wages will be the inverse of the ratio of the number of days required by each to do the work. Hence, the correct answer will be 3:2 → ₹30

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?

Correct Answers :

[A]

Explanation :

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.

8. If 8 boys and 12 women can do a piece of work in
25 days, in how many days can the work be done by 6 boys and 11 women working together?

Correct Answers :

[D]

Explanation :

The data is insufficient, since we only know that the work gets completed in 200 boy days and 300 women days.

9. *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?

Correct Answers :

[A]

Explanation :

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

10. *A* can do a piece of work in 20 days. He works at
it for 5 days and then *B* finishes it in 10 more days. In how many days will *A* and *B* together finish the
work?

Correct Answers :

[A]

Explanation :

In 5 days, *A* would do 25% of the work. Since, *B*
finishes the remaining 75% work in 10 days, we can
conclude that *B*’s work in a day = 7.5%
Thus, (*A* + *B*) = 12.5% per day.
Together they would take 100/12.5 = 8 days.

11. *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?

Correct Answers :

[A]

Explanation :

*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.

12. Twenty workers can finish a piece of work in 30
days. After how many days should 5 workers leave the job so that the work is completed in 35 days?

Correct Answers :

[C]

Explanation :

Total man days required = 600 man -days. If 5 workers
leave the job after ‘n’ days, the total work would be done in 35 days. We have to find the value of ‘n’
to satisfy:

20 x n + (35 – n) x 15 = 600.

Solving for n, we get

20n – 15n + 35 x 15 = 600

5n = 75

n = 15.

13. 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.

Correct Answers :

[B]

Explanation :

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

14. Subhash can copy 50 pages in 10 hours; Subhash and
Prakash together can copy 300 pages in 40 hours. In
how much time can Prakash copy 30 pages?

Correct Answers :

[B]

Explanation :

Subhash can copy 200 pages in 40 hours (reaction to the first sentence). Hence, Prakash can copy 100 pages in 40 hours. Thus, he can copy 30 pages in 30% of the time, i.e., 12 hours.

15. *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?

Correct Answers :

[C]

Explanation :

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

16. Sashi can do a piece of work in 25 days and Rishi
can do it in 20 days. They work for 5 days and then Sashi goes away. In how many more days will Rishi
finish the work?

Correct Answers :

[D]

Explanation :

Sashi = 4%, Rishi = 5%. In five days, they do a total of 45% work. Rishi will finish the remaining 55% work in 11 more days.

17. 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?

Correct Answers :

[C]

Explanation :

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 days (Vicky and Tinku) + 3 days (Tinku alone)

18. Sambhu can do 1/2 of the work in 8 days while Kalu
can do 1/3 of the work in 6 days. How long will it
take for both of them to finish the work?

Correct Answers :

[B]

Explanation :

Sambhu requires 16 days to do the work while Kalu
requires 18 days to do the work.

(1/16 + 1/18) x n = 1

→ n = 288/34 = 144/17

19. 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?

Correct Answers :

[A]

Explanation :

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.

20. An engineer undertakes a project to build a road 15
km long in 300 days and employs 45 men for the purpose. After 100 days, he finds only 2.5 km of the
road has been completed. Find the (approx.) number of extra men he must employ to finish the work in time.

Correct Answers :

[D]

Explanation :

After 100 days and 4500 man days, only 1/6th of the
work has been completed. You can use the product change algorithm of PCG to solve this question.
100 x 45 = 16.66% of the work. After this you have 200 days (i.e., 100% increase in the time available)
while the product 200 x number of men should correspond to five times times the original product.

This will be got by increasing the no. of men by 150% (300/200).

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