A alone can complete a piece of work in 15 days, while B alone can do it in 30 days, if the both of them work on alternate days, when will the work get completed?

Correct option is C

Given:

A alone completes the work in 15 days.

So, A's 1-day work = $$\frac{1}{15}$$​​

B alone completes the work in 30 days.

So, B's 1-day work =$$\frac{1}{30}$$​​

They work on alternate days, starting with A.

Concept Used:

In 2 days, work done = A’s 1-day work + B’s 1-day work.

We continue this cycle until the work is completed.

Solution:

​$$\text{Work done in 2 days} = \frac{1}{15} + \frac{1}{30}$$=$$= \frac{2}{30} + \frac{1}{30} = \frac{3}{30} = \frac{1}{10}$$​​

So, in 2 days, they complete $$\frac{1}{10}$$​ of the work.

Since total work is 1, we calculate the number of full 2-day cycles:

​$$\text{Full cycles needed} = \frac{1}{\frac{1}{10}} = 10 \text{ cycles}$$​​

Each cycle takes 2 days, so:

10×2=20 days

Option (C) is right.