P is thrice as good a workman as Q and therefore able to finish a job in 48 days less than Q. Working together, they can do it in ?

Answer: Option A

Let time taken by P = x days
Then, time taken by Q = 3x days
∴ 3x - x = 48
⇒ 2x = 48
⇒ x = 24
∴ (P + Q)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{24}+\frac{2}{72}\\ & =\frac{3+1}{72}\\ & =\frac{1}{18}\end{array}$$
∴ Required time = 18 days

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Alternate:
Ratio of times taken by P and Q = 1 : 3
The time difference is 3 - 1 = 2 days
while Q take 3 days and P takes 1 day
If difference of time is 2 days, Q takes 3 days
If difference of time is 48 days,
$$\begin{array}{rl}& \text{Q }\text{takes}=\left(\frac{3}{2}\times 48\right)\\ & =72\text{days}\end{array}$$
So, P takes 24 days to do the work.
$$\begin{array}{rl}& \text{P’s 1 day’s work}=\frac{1}{24}\\ & \text{Q’s 1 day’s work}=\frac{1}{72}\\ & \left(\text{P + Q}\right)\text{’s 1 day’s work}\\ & \text{ = }\left(\frac{\text{1}}{24}\text{ + }\frac{\text{1}}{72}\right)=\frac{\text{4}}{72}=\frac{1}{18}\end{array}$$
∴ A and B together can do the work in
$$\frac{18}{1}=\text{18 }\text{days}$$