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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