A and B together can complete a work in 10 days. A alone can do it in 15 days. In how many days can B alone complete the work?

Given:

• A and B together can complete the work in 10 days
• A alone can complete the work in 15 days

Step 1: Daily work rates

Let total work = $1$

• A's one-day work

  $$\frac{1}{15}$$

• (A + B)'s one-day work

  $$\frac{1}{10}$$

Step 2: B's one-day work

LCM of $10$ and $15$ is $30$:

Step 3: Time taken by B alone

If B does $\frac{1}{30}$ work in $1$ day,
then B completes the whole work in:

Final Answer

Correct option: (b) 30 days