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?

Correct option is C

Given:

Pravin’s time = 6 hours

Rishi’s time = 28 hours

Time taken by all three together = 4 hours

Formula Used:

Work per hour = $$\frac1 {\text{ time taken}}$$

Solution:  

Let time taken by Shan is S 

So, 

$$\frac{1}{6} + \frac{1}{28} + \frac{1}{S} = \frac{1}{4}$$​​

​$$\frac{1}{S} = \frac{1}{4} - \left(\frac{1}{6} + \frac{1}{28}\right)$$​​

​$$\frac{1}{S} = \frac{1}{4} - \frac{17}{84} = \frac{21 - 17}{84}$$​​

​$$\frac{1}{S} = \frac{4}{84} = \frac{1}{21}$$​​

Thus,  time take by Shan to complete the work alone = 21 hours 

Alternate Solution: ​

Work = Rate × Time

Total work = LCM of (84, 6, 28) = 84

Pravin’s  work rate = $$\frac{84}{6}$$​ = 14 units

Rishi’s work rate = $$\frac{84}{28}$$​ = 3 units

Combined Work rate by all three = $$\frac{84}{4}$$​ = 21 unit

Now, Shan's work rate = 21 - (14 + 3) = 4 

Shan's time to complete the work alone = $$\frac{84}{4} = 21 \ hours$$​