Question

$3$ men or $5$ women can do a work in $12$ days. How long will $6$ men and $5$ women take to do it?

(a) $6$ days

(b) $5$ days

(c) $4$ days

(d) $3$ days

Answer 1

The coret option is (c): $4$ days

$3$ men $=5$ women

$1$ man $=\frac{5}{3}$ women

$6$ men $=\frac{5}{3}\times 6=10$ women

$\therefore$ Total women in second case. [i.e $6$ men and $5$ women]

$=10+5=15$ women

Now,

$5$ women $\to 12$ days

$15$ women $\to x$ days

$5$ women $:15$ women $::12$ days $:x$

$\therefore$ By inverse proportion

$5:15::x:12$

$x=\frac{5\times 12}{15}=4$ days