Question : P is thrice as good as a workman as Q and therefore can finish a work in 40 days less than Q. In how many days can they together complete the same work?
Option 1: 20 days
Option 2: 15 days
Option 3: 22.5 days
Option 4: 18 days
Correct Answer: 15 days
Solution :
Let Q finish the work in $D$ days then P will finish the same work in $(D - 40)$ days.
So, 1-day work (efficiency) of Q = $\frac{1}{D}$
and 1-day work (efficiency) of P = $\frac{1}{D - 40}$
According to the question
⇒ $\frac{1}{D - 40}$ = 3 × $\frac{1}{D}$
⇒ D = 3(D – 40)
⇒ D = 60
⇒ Q's time = 60 days
⇒ P’s time = 60 − 40 = 20 days
1-day work of P and Q together = P’s 1-day work + Q’s 1-day work
$=\frac{1}{D – 40}$ + $\frac{1}{D}=\frac{1}{20} + \frac{1}{60} = \frac{4}{60}= \frac{1}{15}$
So, time taken by P and Q together = $\frac{1}{\frac{1}{15}}$ = 15 days
Hence, the correct answer is 15 days.
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