Question

If 2 men and 3 boys can do a piece of work in 10 days and 3 men and 2 boys can do it 8 days, how long will 2 men and 1 boy take to do it

• A. 15
• B. 18
• C. 12.5
• D. 16

Answer 1

The correct option is C 12.5

Let men take 'm' days to complete a work and boys take 'b' days to complete the work. So in one day men do $\frac{1}{m}$ job and boys do $\frac{1}{b}$ job

2 men and 3 boys together do a piece of work in 10 days.Therefore we will equate job done in one day by them:

$2\left(\frac{1}{m}\right)+3\left(\frac{1}{b}\right)=\frac{1}{10}$

Similarly 3 men and 2 boys together do it in 8 days.Therefore we will equate piece of work done in one day by 3 men and 2 boys

$3\left(\frac{1}{m}\right)+2\left(\frac{1}{b}\right)=\frac{1}{8}$

Substitute $\frac{1}{m}=p$ and $\frac{1}{b}=q$

So then our 2 equations becomes $2p+3q=\frac{1}{10}$

and $3p+2q=\frac{1}{8}$

Solving simultaneously we get $p=\frac{7}{200}$ and $q=\frac{2}{200}$

So we need to find number of days required to do piece of work by 2 men and 1 boy together i.e

find k such that

$k(2p+q)=1$

Substitute value of p and q:

$k(\frac{14}{200}+\frac{2}{200})=1$

$⟹k=12.5$