Question

$4$ men and $3$ women finish a job in $6$ days. And $5$ men and $7$ women can do the same job in $4$ days. How long will $1$ man and $1$ woman take to do the work?

• A. $22\frac{2}{7}days$
• B. $25\frac{1}{2}days$
• C. $5\frac{1}{7}days$
• D. $12\frac{7}{22}days$

Answer 1

The correct option is

A

$22\frac{2}{7}days$

($4$ men $+3$ women)$\times 6$ days$=$($5$ men $+7$ women)$\times 4$ days

$24$ men $+18$ women$=20$ men $+28$ women

$4$ men days $=10$ women days

$1$ men days $=2.5$ women days ...(i)

Total work to be done $=24$ men days $+18$ women days

$=60$ women days $+18$ women days [From (i)]

$=78$ women days

Work done by $1$ man $+1$ women $=2.5$ women $+1$ women $=3.5$

$\therefore$ Both a man and a woman can complete the entire work in $=\frac{78}{3.5}=22\left(\frac{2}{7}\right)$ days