Arjun can do a piece of work in 4 hours. Kartik can do it in 48 hours. With the assistance of Ishan, they completed the work in 3 hours. In how many hours can Ishan alone do it?

Correct option is D

Given:

Arjun can do the work in 4 hours 

Kartik can do the work in 48 hours 

Together with Ishan, work completed in 3 hours 

Formula Used:

Work rate =$$\frac{1}{\text{time}}$$​

Solution:

Arjun’s rate = $$\frac{1}{4} = \frac{12}{48}$$​​

Kartik’s rate =$$\frac{1}{48}$$​​

Combined rate =$$\frac{1}{3} = \frac{16}{48}$$​​

So,

Ishan’s rate = $$\frac{16}{48} - \left(\frac{12}{48} + \frac{1}{48}\right) = \frac{16}{48} - \frac{13}{48} = \frac{3}{48} = \frac{1}{16}$$​

Ishan’s time=$$\frac{1}{\tfrac{1}{16}} = 16 \ \text{hours}$$​

Ishan alone can do the work in 16 hours.

Alternate Method:

Ishan's time = $$\frac {48}{16-1-12}=\frac{48}{3}=16$$ hours​