Question : 35 men can complete a work in 15 days. 15 women can complete the same work in 35 days. In how many days 9 men and 16 women can complete the work?
Option 1: 15 days
Option 2: 18 days
Option 3: 10 days
Option 4: 21 days
Correct Answer: 21 days
Solution :
Given: 35 men can complete a work in 15 days.
15 women can complete the same work in 35 days.
LCM of 15 and 35 = 105
Let the total work = 105 units
Efficiency of 35 men $=\frac{105}{15} = 7$ units/day
Efficiency of 1 man $=\frac{7}{35} = \frac{1}{5}$ units/day
Efficiency of 15 women $=\frac{105}{35}= 3$ units/day
Efficiency of 1 woman $=\frac{3}{15} = \frac{1}{5}$ units/day
Efficiency of 9 men and 16 women $=(9\times\frac{1}{5}+ 16\times\frac{1}{5})=(\frac{9}{5}+\frac{16}{5})=\frac{25}{5}=5$ units/day
Time taken to complete the work $=\frac{105}{5}=21$ days
Hence, the correct answer is 21 days.
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