Question

Pravin can do a piece of work in 6 hours. Rishi can do it in 28 hours. With the assistance of Shan, they completed the work in 4 hours. In how many hours can Shan alone do it?

• A. 23
• B. 20
• C. 21
• D. 22

Answer 1

Answer:

C. 21

Rate of work = 1 / (time taken to complete the work)

Praveen's speed in one hour: 1/6

Rishi's speed in one hour: 1/28

Praveen, Rishi and Shaan together completed the work in 4 hours.

Therefore, the combined speed of all three in one hour = 1/4

To find Shan's speed in one hour:

(Praveen's speed + Rishi's speed + Shan's speed) = Combined speed of all three

(1/6 + 1/28 + Shan's speed) = 1/4

Shan's speed = 1/4 - (1/6 + 1/28)

= 1/21

The time taken by Shan to complete the work alone is:

Time = 1 / (speed)

Time = 1 / (1/21) = 21 hours