Question : P alone can complete a work in 25 days and Q alone can complete the same work in 50 days. If both of them work together, then in 12 days what percent work of the total work will be completed?
Option 1: 80%
Option 2: 72%
Option 3: 48%
Option 4: 60%
Correct Answer: 72%
Solution :
Time taken by P to do the work = 25 days
Part of work done by P in a day = $\frac{1}{25}$
Time taken by Q to do the work = 50 days
Part of work done by Q in a day = $\frac{1}{50}$
Part of the work done by P and Q in 12 days = 12 × $(\frac{1}{25}+\frac{1}{50})$
= $\frac{12×(2+1)}{50}$
= $\frac{36}{50}$
Required percentage = $\frac{36}{50}$ × 100
= 72%
Hence, the correct answer is 72%.
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