Question

One man can do a piece of work in $3$ hours; another can do the same piece of work in $2$ hours. How long will they take if they work together?

Answer 1

Let one hour work of first man be=x

Let one hour work of other man be =y

Total work to be done $=z=3x=2y$

Let them take n hours to complete the work together

$\Rightarrow n(x+y)=z$

$\Rightarrow n(x+y)=3x$

$\Rightarrow n(x+\frac{3x}{2})=3x$

$\Rightarrow n\left(\frac{5x}{2}\right)=3x$

$\Rightarrow n=\frac{6}{5}=1.2$ hours

or ($1.2\times 60=72$ minute )