Question

$12$ men can complete a piece of work in $4$ days while $15$ women can complete the same work in $4$ days $6$ men start working on the job and after working for $2$ days all of them stopped working. How many women should be put on the job to complete the remaining work if it is to be completed in $3$ days ?

• A. $15$
• B. $18$
• C. $22$
• D. None of these

Answer 1

Answer: (A)

$15$

$12$ men can complete a piece of work in $4$ days

$15$ women can complete the same work in $4$ days
Let the productivity of men be $m$ and the productivity of women be $w$

Thus,

$12m\times 4=15w\times 4$

$=>4m=5w$

$=>m=\frac{5}{4}w$

Total work done by women $=60w$

Work done by 6 men in 2 days $=6m\times 2$

$=6\times \frac{5}{4}\times 2$

$=15w$

Thus, remaining work $=60w-15w$

$=45w$

Let F women complete the remaining job in 3 days

Thus, $Fw\times 3=45w$

$=>F=\frac{45}{3}$

$=>F=15$

Thus, $15$ women are required to complete the job.