Question

if 5 men and 9 women can do a piece of work in 19 days then in how many days will 3 men and 6 women do the same work ?

• A. 12 days
• B. 15 days
• C. 18 days
• D. 21 days

Answer 1

The correct option is B 15 days

It is given that 5 men or 9 women can do the job in 19 days.

So, 5 men=9 women

1 man = $\frac{9}{5}$ women

3 men = 3 $\left(\frac{9}{5}\right)$ women

So, work done = 3 men+6 women = 3 $\left(\frac{9}{5}\right)+6$

$=\frac{27}{5}+6$

$=\frac{57}{5}$

Now,$\frac{M_1{D}_1}{W_1}$= $\frac{M_2{D}_2}{W_2},$

let $D_2=x$

$\frac{9\ast 19}{W_1}=\frac{\frac{57}{5}\ast x}{W_2}$

$⟹9\ast 19=\frac{57x}{5}$

$⟹3=\frac{x}{5}$

$⟹x=15$ days

So, option (b) is correct.