Question : P and Q together can do a work in 12 days. P alone can do the same work in 36 days. In how many days can Q alone complete two-thirds part of the same work?
Option 1: 12
Option 2: 15
Option 3: 18
Option 4: 21
Correct Answer: 12
Solution :
Time taken by P and Q to do the work = 12 days
(P and Q)'s 1 day's work = $\frac{1}{12}$
P alone can do the work in 36 days
P's 1 day's work = $\frac{1}{36}$
Q's 1 day's work = $\frac{1}{12} - \frac{1}{36}=\frac{2}{36}=\frac{1}{18}$
⇒ Q can do the whole work in 18 days
So, $\frac{2}{3}$ work can be done by Q in 18 × ($\frac{2}{3}$) = 12 days
Hence, the correct answer is 12.
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