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. $41$

Answer 1

Answer: (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 $=(\frac{41}{48}\times 48)=41$.