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Time and Work

A man, a woma...

Question

A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and I women to complete the job in $\frac{1}{4}$ of a day ?

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Solution

The correct option is D 41
1 man's 1 days work = $\frac{1}{3}$ 1 woman's 1 days' work = $\frac{1}{4}$
1 boy's 1 days' work = $\frac{1}{12}$ Let the number of boys to assist be x Then $\frac{1}{3} + \frac{1}{4} + \frac{x}{12} = \frac{1}{1 / 4}$
$\Rightarrow \frac{4 + 3 + x}{12} = 4 \Rightarrow 7 + x = 48 \Rightarrow x = 41$ boys

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A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and I women to complete the job in 14 of a day ?

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