Question

$16$ men or $24$ women can do a piece of work in $20$ days. The number of days needed to complete the job, if $20$ men and $30$ women are employed to do the same piece of work is

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is C $8$

$16\left(M\right)$ or $24\left(W\right)$ women can do a piece of work in $21$ day.

$\therefore 16M\equiv 24W$

$\Rightarrow 2M=3W$ (devide both sides by $8$)

$\Rightarrow 20M=30W$ (Multiply both sides by $10$)

$\because 20M\equiv 30W$

$\therefore$ total number of people to complete the work

$20$ men+$30$women

$=30$ women+$30$ women

$=60$ women

$\because 24$ women can do a piece of work in $20$ days.

$\therefore$ Let $60$ women can do a piece of work in $x$ days.

$\therefore 24\times 20=60\times x$

$⟹x=\frac{24\times 20}{60}=8$ days.

Formula:

If $M_1$ people do $x$ piece of work in $D_1$ days and $M_2$ people do $x$ piece of work in $D_2$ days

$\therefore M_1{D}_1=M_2{D}_2$