Question : P is two times more efficient than Q. P can complete a piece of work in 40 days less than Q. Working together, the whole number of days taken by them to complete the work is:
(Round off to the nearest integer)
Option 1: 26
Option 2: 25
Option 3: 27
Option 4: 28
Correct Answer: 27
Solution :
Let the time taken by Q and P to complete the work be $x$ days and ($x - 40$) days respectively.
Given: That P is two times more efficient than Q.
So, $\frac{1}{x-40}=\frac{2}{x}$
⇒ $x = 2(x - 40)$
⇒ $x = 80$
From the above value, Q alone can complete the work in 80 days and P alone can complete the work in 40 days.
The combined work of P and Q in 1 day = $\frac{1}{40} + \frac{1}{80} = \frac{3}{80}$.
And the number of days required for P and Q together can complete the work = \(\frac{80}{3} \approx 27\) days
Hence, the correct answer is 27.
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