Question : 15 men and 25 women can complete a piece of work in 9.6 days. If 16 women can complete the same work in 27 days, find the number of days in which 16 men can complete the same work.
Option 1: 22.50
Option 2: 20.25
Option 3: 19.20
Option 4: 21.60
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Correct Answer: 20.25
Solution :
Given: 15 men and 25 women can complete a piece of work in 9.6 days.
16 women can complete the same work in 27 days.
Assuming the efficiency of a man is $M$ and that of a woman is $W$.
According to the question,
⇒ $(15M+25W)×9.6=16W×27$
⇒ $30M+50W=90W$
⇒ $30M=40W$
⇒ $3M=4W$
⇒ $\frac{M}{W}=\frac{4}{3}$
So, efficiency of men = 4 units
Efficiency of women = 3 units
Total work = 16 × 3 × 27 units
16 men can do the total work = $\frac{16×3×27}{16×4}=\frac{81}{4}$ = 20.25 days
Hence, the correct answer is 20.25.
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