Anil can do a piece of work in 4 hours. Ashok can do it in 8 hours. With the assistanceof Robin, they completed the work in 2 hours. In how many hours can Robin alone doit?

Correct option is C

Given:

Anil can do the work in 4 hours.

Ashok can do the work in 8 hours.

With the assistance of Robin, they completed the work in 2 hours.

Solution:

Rate of work of Anil = $$\frac{1}{4}$$​​

Rate of work of Ashok = $$\frac{1}{8}$$​​

Rate of work of Robin = $$\frac{1}{r}$$​ 

Combined rate of work =$$\frac{1}{2}$$​​

The total rate of work when Anil, Ashok, and Robin work together is the sum of their individual rates:

​$$\frac{1}{4} + \frac{1}{8} + \frac{1}{r} = \frac{1}{2}$$​​

​$$\frac{2}{8} + \frac{1}{8} + \frac{1}{r} = \frac{1}{2}$$​​

​$$\frac{3}{8} + \frac{1}{r} = \frac{1}{2}$$​​

​$$\frac{1}{r} = \frac{1}{2} - \frac{3}{8}$$​​

​$$\frac1r = \frac{4 -3}{8}$$​​

​$$\frac{1}{r} = \frac{1}{8} \quad \Rightarrow \quad r = 8$$​​

Robin alone can complete the work in 8 hours.

Alternate Solution: 

Total Work = LCM of 8, 4, 2 = 8 

Efficiency of Anil = $$\frac84=2$$

Efficiency of Ashok = $$\frac88=1$$

Combined Efficiency = $$\frac82=4$$ 

Robin's Efficiency = 4 - (2+1) = 1 

Robin's time = $$\frac{8}1 = 8 \ hours$$​​