Question : A man is twice as fast as a woman and twice as fast as a boy at doing work. If all of them a man, a woman, and a boy can finish the work in 7 days, in how many days will a boy do it alone?
Option 1: 49
Option 2: 7
Option 3: 6
Option 4: 42
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Correct Answer: 49
Solution : Given: A man is twice as fast as a woman and twice as fast as a boy at doing work. According to the question, 1 man = 2 women = 4 boys The efficiency of man : woman : boy = 4 : 2 : 1 Taking for a boy, $\therefore$ 1 man + 1 woman + 1 boy are equivalent to (4 + 2 + 1 = 7 boys). We know, that M 1 D 1 = M 2 D 2 , where M 1 and M 2 are the number of boys and D 1 and D 2 are their respective times to finish the work. ⇒ 7 × 7 = 1 × D 2 $\therefore$ D 2 = 49 days Hence, the correct answer is 49.
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