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?
Answer & explanation
Correct answer: option 2
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.