Mohan can do a piece of work in 9 hours. Pramod can do it in 21 hours. With the assistance of Ashish, they completed the work in 6 hours. In how many hours can Ashish alone do twice the same work?​

Correct option is B

Given:

Mohan's time = 9 hours 

Pramod's time = 21 hours 

All three together complete the work in 6 hours

Concept Used:

Work done per unit time is additive. If total work is 1 unit

Solution:

Work rate of Ashish = $$\frac{1}{6} - \left(\frac{1}{9} + \frac{1}{21}\right)$$​​

​$$= \frac{21 - 14 - 6}{126}$$​​

​$$= \frac{1}{126}$$​​

So, Ashish alone does the work in 126 hours.

For twice the same work = 2 $$\times$$​ 126 = 252 hours

Alternate Solution: ​

Total work = LCM(9, 21, 6) = 126

Mohan's efficiency = $$\frac{126}{9}$$​ = 14 units/hour

Pramod's efficiency = $$\frac{126}{21}$$​ = 6 units/hour

All three together = $$\frac{126}{6}$$​ = 21 units/hour

Ashish’s efficiency = 21 - (14 + 6) = 1 unit/hour

Time taken by Ashish to do twice the work = $$\frac{2 \times 126}{1}$$​ = 252 hours