A and B can together complete a task in 16 days. They started a task together, and after 4 days A leave, B takes 24 days to finish the rest of the task. How many days would B have taken to do the task if he worked alone?

Correct option is C

Given:
A and B can together complete a task in 16 days
They started a task together and after 4 days A leave, B takes 24 days to finish the rest of the task.
Formula Used:
Work = Time × Efficiency
Solution:
Let the efficiency of A and B be a and b respectively.
Total work = (a + b) × 16
Work done by A and B together = 4 × (a + b)
Remaining work done by B = 24 × b  

Total work = work done by A + B together in 16 days = work done by ( A + B) × 4 + work done by B in 24 days 

So,   
4 × (a + b) + 24 × b = (a + b) × 16
a = b
Then, time taken by B alone to finish work =$$\frac{(1 + 1) \times 16}{1}$$​ = 32 days.