Question

$4$ men or $6$ women can do a work in $42$ days. The number of days $12$ men and $3$ women would take to finish the work is

• A. $20$ days
• B. $15$ days
• C. $12$ days
• D. $10$ days

Answer 1

Answer: (C)

$12$ days

Let the amount of work done by $1$ man in a day be $m$, and that done by $1$ woman be $w$.

Now, $4m=6w$

Or, $w=\frac{2m}{3}\dots \dots \dots \left(1\right)$

Also, amount of work done by $4$ men in a day $=4m$

Or $4m=\frac{1}{42}$

Or, $m=\frac{1}{168}\dots \dots \dots \left(2\right)$

Using $\left(1\right)$ and $\left(2\right)$, amount of work done by $12$ men and $3$ women in a day is $12m+3w$

$=12m+2m$ (substituting $w$ from $1$)

$=14m$

$=14/168$

$=1/12$

So, the total work will be completed in $12$ days.