Kartik can do a piece of work in 4 hours. Ishan can do it in 20 hours. With theassistance of Krish, they completed the work in 2 hours. In how many hours can Krishalone do it?

Correct option is C

Given:

Kartik can do the work in 4 hours 

Ishan can do it in 20 hours 

All three together completed the work in 2 hours 

Solution: 

Kartik work rate = $$\frac{1}{4}$$​​

Ishan rate = $$\frac{1}{20}$$​​

Kartik + Ishan + Krish combined rate = $$\frac{1}{2}$$​​

Let Krish’s rate be $$\frac{1}{x},$$​ Then:

​$$\frac{1}{4} + \frac{1}{20} + \frac{1}{x} = \frac{1}{2}$$​​

​$$\frac{5 + 1}{20} + \frac{1}{x} = \frac{1}{2}$$​​

​$$\frac{6}{20}+ \frac{1}{x} = \frac{1}{2}$$​​

​$$\frac{1}{x} = \frac{1}{2} - \frac{6}{20}$$​​

​$$\frac{1}{x} = \frac{1}{2} - \frac{3}{10}$$​​

​$$\frac{1}{x} = \frac{5 - 3}{10}$$​​

​$$\frac{1}{x} = \frac{2}{10}$$​​

​$$\frac{1}{x} = \frac{1}{5}$$​​

Thus, Ishan time to complete the work is 5 hours

Alternate Solution: ​

total work = LCM of 4, 20, and 2 = 20 units

Kartik's rate = $$\frac{20}{4}$$​ = 5 units/hour

Ishan's rate = $$\frac{20}{20}$$​ = 1 unit/hour

All three together = $$\frac{20}{2}$$​ = 10 units/hour

Now , Krish's rate = 10 - (5 + 1) = 4 units/hour

So, time taken by Krish alone = $$\frac{20}{4}$$​= 5 hours