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?

240 days

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.