Question

Sita can finish typing a $100$ page document in $9$ hours. Mita in $6$ hours and Rita in $12$ hours. How long will they take to type a $100$ page document if they work together?

Answer 1

Time taken by Sita to do the work $=9$ hours

Time taken by Mita to do the work $=6$ hours

Time taken by Rita to do the work $=12$ hours

Now,Work done by Sita in $1$ hour $=\frac{1}{9}$

Work done by Mita in $1$ hour $=\frac{1}{6}$

Work done by Rita in $1$ hour $=\frac{1}{12}$

$\therefore$ Work done by them together in $1$ hour $=\frac{1}{9}+\frac{1}{6}+\frac{1}{12}=\frac{4+6+3}{36}=\frac{13}{36}$ [L.C.M of $9,6,12$ is $36$]

Thus, together they can do the work (typing $100$ pages) in $\frac{36}{13}=2\frac{10}{13}$ hours.