A and B working together can finish a piece of work in 12 days while B alone can finish the same work in 30 days. Then determine that in how many days can A alone finish the same work?

20 days

The correct answer is Option (2) → 20 days

Let the total work be 1 unit.

• A + B can finish the work in 12 days

$\Rightarrow \text{Rate of (A+B)} = \frac{1}{12}$

• B alone can finish the work in 30 days

$\Rightarrow \text{Rate of B} = \frac{1}{30}$

So, rate of A:

$\frac{1}{12} - \frac{1}{30}$​

LCM of 12 and 30 = 60

$= \frac{5 - 2}{60} = \frac{3}{60} = \frac{1}{20}$

Thus, A alone can finish the work in 20 days.