Question : If 3 boys and 8 girls can do work in 6 days, and 1 boy and 5 girls can finish the same in 12 days, find the ratio of efficiencies of a boy and a girl.
Option 1: 2 : 1
Option 2: 1 : 5
Option 3: 2 : 5
Option 4: 3 : 2
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Correct Answer: 2 : 1
Solution : Given: 3 boys and 8 girls can do work in 6 days, and 1 boy and 5 girls can finish the same in 12 days. Let the efficiencies of a boy and a girl be $x$ and $y$ respectively. Work done = Time × Efficiency According to the question, ⇒ $(3x + 8y)\times 6=(x+5y)\times 12$ ⇒ $18x+48y=12x+60y$ ⇒ $18x-12x=60y-48y$ ⇒ $6x=12y$ ⇒ $x=2y$ ⇒ $x:y=2:1$ Hence, the correct answer is 2 : 1.
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