Question : A man and a woman can finish a work together in half the time taken by a woman and a boy together. A boy can finish the work alone in 20 days and 2 women together can finish it in 30 days. In how many days will the work be finished by 4 men?
Option 1: 2
Option 2: 2.14
Option 3: 2.5
Option 4: 3
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Correct Answer: 2.14
Solution : Given: Time taken by a man and a woman = $\frac{1}{2}$ (Time taken by a woman and a boy) Time taken by a boy to complete the work = 20 days Time taken by 2 women to complete the work = 30 days Time taken by a woman to complete the work = 60 days Let a man finish the work in $m$ days The time taken by a woman and a boy to complete the work is $x$ days. Then, $\frac{1}x = \frac{1}{60}+\frac{1}{20}$ ⇒ $x$ = 15 days Now, time taken by a man and a woman =$\frac{15}{2}$ days So, ${\frac{1}m+\frac{1}{60}}=\frac{2}{15}$ ⇒ $m=\frac{60}7$ Time taken by 4 men to do the work $=\frac{m}4=\frac{15}{7}=2.14$ days Hence, the correct answer is 2.14.
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