Question

A particular work can be completed by $6$ men and $6$ women in $24$ days, whereas the same work can be completed by $8$ men and $12$ women in $15$ days. Find the time taken by $4$ men and $6$ women to complete the same work .

• A. $20$ days
• B. $30$ days
• C. $50$ days
• D. $40$ days

Answer 1

The correct option is B $30$ days

From the question, we have
($6$ men and $6$ women) $1$ day work $=\frac{1}{24}$

($12$ men and $12$ women)$1$ day work$=\frac{1}{12}$ ... (1)

($8$ men and $12$ women)$1$ day work$=\frac{1}{15}$ ... (2)
Subtracting (1) and (2), we get
$4$ men work $=\frac{1}{12}$ $-\frac{1}{15}$$=\frac{1}{60}$

$2$ men work $=\frac{1}{120}$

$4$ men and $6$ women work $=1$ day work of $6$ men and $6$ women $-1$ day work of $2$ men.

$=\frac{1}{24}$ $-\frac{1}{120}$$=\frac{4}{120}$ $=\frac{1}{30}$

The time taken by $4$ men and $6$ women to complete the same work $=30$ days.

Hence, option B.