A and B together can complete a task in 36 days. If B stops working after 30 days, the task will be completed in total 40 days. A alone can complete the task in:

Correct option is A

Given:

A and B together can complete a task in 36 days.

B stops working after 30 days.

The task is completed in a total of 40 days.

Concept Used:

Work done = Efficiency × Time

If someone works for 'n' days, the work done = n × Efficiency

Solution:

Let A's one-day work (efficiency) be 'a' and B's one-day work (efficiency) be 'b'.

A and B together can complete the work in 36 days.

So, (a + b) × 36 = 1 (Complete work)

a + b =$$\frac {1}{36}$$​ ---- (1)

B works for 30 days and A works for 40 days to complete the work.

So, 40a + 30b = 1 ---- (2)

Multiply equation (1) by 30:

30a + 30b =$$\frac{ 30}{36} =\frac 56$$​ ---- (3)

Subtract equation (3) from equation (2):

(40a + 30b) - (30a + 30b) = 1 - $$\frac 56$$​​

10a = $$\frac 16$$​​

a =$$\frac{1}{60}$$​​

Therefore, A alone can complete the task in 60 days.