Question : P and Q together can do a work in 12 days. P alone can do the same work in 18 days. In how many days can Q alone complete two-thirds part of the same work?
Option 1: 30
Option 2: 21
Option 3: 24
Option 4: 36
Correct Answer: 24
Solution :
Time taken by P alone to complete a work = 18 days
Part of work done by P alone in a day = $\frac{1}{18}$
Let $x$ be the time Q alone takes to complete a work.
Part of work done by Q alone in a day = $\frac{1}{x}$
Time taken by P and Q together to complete a work = 12 days
Part of work done by P and Q together in a day = $\frac{1}{12}$
So, $\frac{1}{18} + \frac{1}{x} = \frac{1}{12}$
$⇒\frac{1}{x} = \frac{1}{12} - \frac{1}{18} = \frac{3-2}{36} = \frac{1}{36}$
Time taken by Q alone to complete the work = 36 days
Time taken by Q alone to complete two-thirds of the work = $\frac{2}{3}$ × 36 = 24 days
Hence, the correct answer is 24.
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