Deepak alone can do a work in 24 hours. Deepak and Rohit together can do the same work in 20 hours. Rohit and Tarun together can do the same work in 16 hours. In how many hours can Tarun alone do the same work?

Correct option is A

Given:
Deepak alone can do the work in 24 hours.

Deepak and Rohit together can do the same work in 20 hours.
Rohit and Tarun together can do the same work in 16 hours.
Concept Used:
Work and Time: If a person can complete a work in  x  hours, their work rate is $$\frac{1}{x}$$​(work per hour).
When multiple people work together, their work rates add up.
Solution:
Deepak alone can complete the work in 24 hours.
So, Deepak's work rate =$$\frac{1}{24}$$​ (work per hour).
Deepak and Rohit together can complete the work in 20 hours.
So, their combined work rate =$$\frac{1}{20}$$​ (work per hour).
Let Rohit's work rate be $$\frac{1}{R}$$​​
From Step 1 and Step 2:
​$$\frac{1}{24} + \frac{1}{R} = \frac{1}{20}$$​​

​$$\frac{1}{R} = \frac{1}{20} - \frac{1}{24}$$​​

​$$\frac{1}{R} = \frac{6 - 5}{120} = \frac{1}{120}$$​​
So, Rohit's work rate =$$\frac{1}{120}$$​ (work per hour).
This means Rohit alone can complete the work in 120 hours.
Rohit and Tarun together can complete the work in 16 hours.
So, their combined work rate $$= \frac{1}{16}$$​(work per hour).
Let Tarun's work rate be $$\frac{1}{T} .$$​
From Step 3 and Step 4:
​$$\frac{1}{120} + \frac{1}{T} = \frac{1}{16}$$​​

​$$\frac{1}{T} = \frac{1}{16} - \frac{1}{120}$$​

​$$\frac{1}{T} = \frac{15 - 2}{240} = \frac{13}{240}$$​​
So, Tarun's work rate $$= \frac{13}{240}$$​(work per hour).
This means Tarun alone can complete the work in:
T $$= \frac{240}{13}$$​​
Tarun alone can complete the work in $$\frac{240}{13}$$​ hours, 
Alternate Method:
Let the total work be LCM of 24, 20, and 16 = 240 units.
Deepak's work rate =$$\frac{240}{24}$$​ = 10 units/hour.
Deepak and Rohit's combined work rate = $$\frac{240}{20} = 12$$​units/hour.
So, Rohit's work rate = 12 - 10 = 2 units/hour.
Rohit and Tarun's combined work rate =  $$\frac{240}{16} = 15$$​ units/hour.
So, Tarun's work rate = 15 - 2 = 13 units/hour.
Thus, Tarun alone can complete the work in:
=$$\frac{240}{13}\text{hours}.$$​