P can build a wall in the same time in which Q and R together can do it. If P and Q together could do it in 30 days and R alone in 40 days, in what time could Q alone do it?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 240 days
Let the total work = 1 wall.
Given:
- $P = Q + R$
- $P + Q$ can do the work in 30 days ⟹ rate = $\frac{1}{30}$
- RRR alone can do the work in 40 days ⟹ rate = $\frac{1}{40}$
From $P = Q + R$:
$P + Q = (Q + R) + Q = 2Q + R$
So,
$2Q + R = \frac{1}{30}$
Substitute $R = \frac{1}{40}$:
$2Q + \frac{1}{40} = \frac{1}{30}$
$2Q = \frac{1}{30} - \frac{1}{40}$
$2Q = \frac{4 - 3}{120} = \frac{1}{120}$
$Q = \frac{1}{240}$
So, Q alone can do the work in 240 days.