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

• A. 1
• B. 4
• C. 19
• D. 41
• E. 6

Answer 1

The correct option is D

41

(1 man + 1 woman)’s 1 day’s work =$(\frac{1}{3}+\frac{1}{4})=\frac{7}{12}$

Work done by 1 man and 1 woman in $\frac{1}{4}$ day=$(\frac{7}{12}\times \frac{1}{4})=\frac{7}{48}$

Remaining work = $(1-\frac{7}{48})=\frac{41}{48}$

Work done by 1 boy in $\frac{1}{4}$ day= $(\frac{1}{12}\times \frac{1}{4})=\frac{1}{48}$

$\therefore$ Number of boys required = $(\frac{41}{48}\times 48)=41$