Question : 10 women can do a piece of work in 6 days, 6 men can do the same work in 5 days, and 8 children can do it in 10 days. What is the ratio of the efficiency of a woman, a man, and a child, respectively?
Option 1: 4 : 6 : 3
Option 2: 4 : 5 : 3
Option 3: 2 : 4 : 3
Option 4: 4 : 8 : 3
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Correct Answer: 4 : 8 : 3
Solution :
Let the efficiency of women, men, and children be $w, m, c$.
10 Women can do the work in 6 days.
⇒ Work done by 1 woman in 1 day = $w = \frac{1}{10\times 6}= \frac{1}{60}$
Similarly, $m = \frac{1}{30}$ and $c = \frac{1}{80}$
So, $w:m:c = \frac{1}{60}: \frac{1}{30}:\frac{1}{80} = \frac{1}{6}: \frac{1}{3}: \frac{1}{8}$
Now, multiplying by LCM(6, 3, 8) = 24
= $24\times \left ( \frac{1}{6}:\frac{1}{3}:\frac{1}{8} \right )$
= 4 : 8 : 3
Hence, the correct answer is 4 : 8 : 3.
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