A alone can complete a task in 30 days, while B alone can complete it in 40 days. A and B, working together, can complete the same task in:

Correct option is A

Given:

A can complete the task in 30 days.

B can complete the task in 40 days. We are asked to find the time taken by A and B working together to complete the task.

Concept Used:

The combined work rate of A and B is:

Combined work rate$$= \frac{1}{\text{Time taken by A}} + \frac{1}{\text{Time taken by B}}$$​

Time taken by A and B together =$$\frac{1}{\text{Combined work rate}}$$​

Solution:

The work rate of A is $$\frac{1}{30}$$​ (since A completes the task in 30 days).

The work rate of B is $$\frac{1}{40}$$​ (since B completes the task in 40 days).

Combined work rate = $$\frac{1}{30} + \frac{1}{40}$$​

​$$\frac{1}{30} + \frac{1}{40} = \frac{4}{120} + \frac{3}{120} = \frac{7}{120}$$​

Time taken by A and B together = $$\frac{120}{7} = 17\frac 17$$​ days

Alternate Method: 

Time taken by A and B together =$$\frac{120}{7} = 17\frac 17$$​ days