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 ?

Solution(By Examveda Team)

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
$$\eqalign{ & = \frac{1}{{24}} + \frac{2}{{72}} \cr & = \frac{{3 + 1}}{{72}} \cr & = \frac{1}{{18}} \cr} $$
∴ 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,
$$\eqalign{ & {\text{Q }}{\kern 1pt} {\text{takes}} = {\text{ }}{\kern 1pt} \left( {\frac{3}{2} \times 48} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 72\,{\kern 1pt} {\text{days}} \cr} $$
So, P takes 24 days to do the work.
$$\eqalign{ & {\text{P's 1 day's work}} = \frac{1}{{24}} \cr & {\text{Q's 1 day's work}} = \frac{1}{{72}} \cr & \left( {{\text{P + Q}}} \right){\text{'s 1 day's work}} \cr & {\text{ = }}\left( {\frac{{\text{1}}}{{24}}{\text{ + }}\frac{{\text{1}}}{{72}}} \right) = \frac{{\text{4}}}{{72}} = \frac{1}{{18}} \cr} $$
∴ A and B together can do the work in
$$\frac{{18}}{1} = {\text{18 }}{\kern 1pt} {\text{days}}$$