A alone can finish a task in 30 days. He works for 6 days on the same task and then B finishes it in 24 days. In how many days can A and B together finish the task?

Correct option is B

Given:
A can finish a work = 30 days

B finishes the remaining task in 24 days after A works for 6 days.

Formula used:

Total work = efficiency × time

Solution:

According to the question:

A can finish the task in 30 days, so the total work is:

​Total work= A×30

In 6 days, A does

A $$\times$$ 6

​The remaining work = $$A\times30-A\times6 = A×24.$$

​​Work done by B in 24 days 

B completes the remaining A×24A \times 24$$A \times 24$$​ work in 24 days.

So, B’s efficiency is:​

B = $$\frac{A \times 24}{24}$$ = A

​Thus, A and B have the same efficiency.

Total time taken by A and B together-

When A and B work together, their combined efficiency is:

A+B = A+A= 2A

The total time taken to finish the task together is:

Total time = $$\frac{Total \ work}{Combined\ efficiency}$$ = $$\frac{30A}{2A}$$ = 15 days

A and B together can finish the task in 15 days.​

Alternate Solution:
A's work rate = $$\frac{1}{30}$$​ tasks per day, In 6 days, A completes $$\frac{6}{30}$$​ = $$\frac{1}{5}$$​ of the task
Remaining work = 1 - $$\frac{1}{5}$$​  = $$\frac{4}{5}$$​​
B finishes $$\frac{4}{5}$$​ of the task in 24 days, so B's rate = $$\frac{\frac{4}{5}}{24}$$​ = $$\frac{1}{30}$$​ tasks per day
A + B's combined rate = $$\frac{1}{30}$$​+ $$\frac{1}{30}$$​ = $$\frac{1}{15}$$​ tasks per day
Time for A and B together to finish the task = $$\frac{1}{\frac{1}{15}}$$​​
= 15 days