Krish can do a piece of work in 3 hours. Moksh can do it in 24 hours. With the assistance of Nitin, they completed the work in 2 hours. In how many hours can Nitin alone do it?

Correct option is B

Given:

Krish can complete the work in 3 hours.

Moksh can complete the work in 24 hours.

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

Formula Used:
Work rate =$$\frac1 {\text{ Time taken}}$$​​

Solution:

Krish's work rate = $$\frac 13$$​(since Krish can complete the work in 3 hours)

Moksh's work rate = $$\frac1{24}$$​ (since Moksh can complete the work in 24 hours)

Let Nitin's work rate be $$\frac 1x$$​ (where x is the time Nitin takes to complete the work alone).

Since together they complete the work in 2 hours, their combined work rate is $$\frac 12.$$​​

So,
$$\frac{1}{3} + \frac{1}{24} + \frac{1}{x} = \frac{1}{2}$$​​

$$\frac{8}{24} +\frac{1}{24} + \frac{1}{x} = \frac{1}{2} \\ \ \\\frac{3}{8} + \frac{1}{x} = \frac{1}{2} \\ \ \\\frac{1}{x} = \frac{1}{2} - \frac{3}{8} = \frac{4}{8} - \frac{3}{8} = \frac{1}{8}$$​

Thus, x = 8.

So, Nitin can complete the work in 8 hours.

Alternate Method:

Let the total work be the LCM of 3, 24, and 2, which is 24 units.

Efficiency of Krish =$$\frac{24}{3} =$$​ 8 units/hour

Efficiency of Moksh =$$\frac{24}{24} =$$​ 1 unit/hour

Together, Krish, Moksh, and Nitin complete 24 units of work in 2 hours, so their combined efficiency is:

Efficiency of Krish + Efficiency of Moksh + Efficiency of Nitin =$$\frac{24}{2}$$​ = 12 units/hour

Efficiency of Nitin = 12 - (8 + 1) = 12 - 9 = 3 units/hour

Time taken by Nitin =$$\frac{\text{Total work}}{\text{Efficiency of Nitin}} = \frac{24}{3} = 8$$​hours

Therefore, Nitin alone can complete the work in 8 hours.