Time and Work Practice Questions

5 questions per page • Detailed step-by-step solutions

Question 6
Medium
A, B, C, and D can do a piece of work in 20 days. If A and B can do it together in 50 days, and C alone in 60 days, find the time in which D alone can do it.
A 75 days
B 60 days
C 100 days
D 80 days
Correct Answer: A

Explanation:

D = 1/20 − 1/50 − 1/60 = (15 − 6 − 5)/300 = 4/300 = 1/75 → 75 days.
Question 7
Medium
If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the rate 22 : 25, then the ratio by which the total wages of the workers should be decreased is = ?
A 6 : 5
B 5 : 6
C 22 : 25
D 11 : 15
Correct Answer: A

Explanation:

Total wages ∝ workers × wage: old : new = 15 × 22 : 11 × 25 = 330 : 275 = 6 : 5.
Question 8
Easy
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
A 6 days
B 7 days
C 8 days
D 10 days
Correct Answer: B

Explanation:

1 woman = 1/70, 1 child = 1/140. 5/70 + 10/140 = 1/14 + 1/14 = 1/7 → 7 days.
Question 9
Easy
In the beginning, Ram works at a rate such that he can finish a piece of work in 24 hrs, but he only works at this rate for 16 hrs. After that, he works at a rate such that he can do the whole work in 18 hrs. If Ram is to finish this work at a stretch, how many hours will he take to finish this work?
A 24 hours
B 21 hours
C 20 hours
D 22 hours
Correct Answer: D

Explanation:

In 16 hours at the first rate Ram does 16/24 = 2/3. The remaining 1/3 at the second rate takes (1/3) × 18 = 6 hours. Total = 16 + 6 = 22 hours.
Question 10
Hard
A and B do a work in exactly 16 days, B and C do the same work in exactly 12 days while C and A do the same work in about 10 days. If A, B and C can together do the work in integral number of days, then C does the work alone in
A 20 days
B 24 days
C 16 days
D 15 days
Correct Answer: C

Explanation:

2(A + B + C) ≈ 1/16 + 1/12 + 1/10 = 59/240 → A + B + C ≈ 59/480 → about 8.1 days. Since the time is an integer, A + B + C = 1/8. C = 1/8 − (A + B) = 1/8 − 1/16 = 1/16 → C alone takes 16 days.