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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 1 woman to complete the job in \(\frac{1}{4}\) of a day ? 

(a) 1 

(b) 4 

(c) 19 

(d) 41

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(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

\(\frac{1}{3}\)\(\frac{1}{4}\)\(\frac{X}{12}\) = \(\frac{1}{\frac{1}{4}}\)

\(\Rightarrow\) \(\frac{4+3+X}{12}\) = 4

\(\Rightarrow\) 7 + x = 48

\(\Rightarrow\) x = 41 boys

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