Question

Ten women can complete a piece of work in $15$ days. Six men can complete the same piece of work in $10$ days. In How many days can $5$ women and six men together complete the piece of work?

• A. $15$ days
• B. $7.5$ days
• C. $9$ days
• D. $12.5$ days

Answer 1

The correct option is B $7.5$ days

$10$ women can complete a piece of work in $15$ days.
$\therefore$ $1$ woman can complete in 1 day $\frac{1}{10\times 15}=\frac{1}{150}$ par of work.
$6$ men can complete the same work in $10$ days

$\therefore$ $1$ man can complete in $1$ day $\frac{1}{6\times 10}=\frac{1}{60}$ part of the work.
$\therefore$ $(6$ men's $+5$ women's$)$ $1$ days' work $=\frac{6}{60}+\frac{5}{150}$

$=\frac{1}{10}+\frac{1}{30}$

$=\frac{3+1}{30}$

$=\frac{4}{30}=\frac{2}{15}$
$\therefore$ $6$ men and $5$ women can complete the whole work in $\frac{15}{2}=7.5$ days.