Nitin can do a piece of work in 7 hours. Pravin can do it in 21 hours. With the assistance of Rishi, they completed the work in 3 hours. In how many hours can Rishi alone do it?

Correct option is B

Given:

Nitin's time = 7 hours

Pravin's time = 21 hours

Total time (all three) = 3 hours

Solution:

Nitin’s 1 hour work = $$\frac{1}{7}$$​​

Pravin’s 1 hour work = $$\frac{1}{21}$$​​

Combined work of all three in 1 hour = $$\frac{1}{3}$$​​

Rishi’s 1 hour work = $$\frac{1}{3} - \left( \frac{1}{7} + \frac{1}{21}\right)$$​​

​$$= \frac{4}{21}$$​​

Rishi's 1 hour work = $$\frac{1}{3} - \frac{4}{21}$$​​

​$$= \frac{7 - 4}{21} = \frac{3}{21} = \frac{1}{7}$$​​

So, Rishi alone can do the work in 7 hours.

Alternate Solution:

Let total work = LCM of 7 and 21 = 21 units

Work = Time × Rate

Nitin's rate = $$\frac{21}{7}$$​= 3 units/hour

Pravin's rate =$$\frac{21}{21}$$​ = 1 unit/hour

Combined rate of all three =$$\frac{21}{3}$$​ = 7 units/hour

Rishi's rate = 7 - (3 + 1) = 3

So, Rishi alone would take = $$\frac{21}{3}$$​= 7 hours