Rishi can do a piece of work in 8 hours. Shan can do it in 12 hours. With the assistanceof Veer, they completed the work in 3 hours. In how many hours can Veer alone do it?

Correct option is A

Given:

Rishi can do the work in 8 hours

Shan can do the work in 12 hours

Together with Veer, they complete the work in 3 hours

Formula Used:

Work Rate = $$\frac{1}{\text{Time Taken}}$$​​

Solution:

Work rate of Rishi =$$\frac{1}{8}$$​​

Work rate of Shan = $$\frac{1}{12}$$​​

Let Veer's work rate be $$\frac{1}{x}$$​​

Total work rate of all three = $$\frac{1}{3}$$​​

So,

​$$\frac{1}{8} + \frac{1}{12} + \frac{1}{x} = \frac{1}{3}$$​​

​$$\frac{1}{x} = \frac{1}{3} - \left( \frac{3}{24} + \frac{2}{24}\right)$$​​

​$$\frac{1}{x} = \frac{1}{3} - \frac{5}{24}$$​​

​$$\frac{1}{x} = \frac{8 - 5}{24}$$​​

​$$\frac{1}{x} = \frac{3}{24} = \frac{1}{8}$$​​

So, x = 8

Thus, Veer alone can do the work in 8 hours. 

Alternate Solution: ​

Work rate = $$\frac{\text{Total Work}}{\text{Time Taken}}$$​​

Assume total work = LCM of 8, 12, and 3 = 24 units

Rishi's 1-hour work =$$\frac{24}{8}$$​ = 3 units/hour

Shan's 1-hour work =$$\frac{24}{12}$$​ = 2 units/hour

Together they complete 24 units in 3 hours

Total rate = $$\frac{24}{3}$$​ = 8 units/hour

Veer’s rate = 8 − (3 + 2) = 3units/hour

Time taken by Veer alone = $$\frac{24}{3}$$​ = 8 hours