Question

Raju&tom together can do a work in 10 day. Tom&appu together can do it in 12 days .appu&raju together can do it in 15 days.in how many days will they finish it if all the three work together?

Answer 1

Answer: All the three will complete the work together in 8 days.

Explanation:

Let together they will complete the work in t days. So one day they will work $\frac{1}{t}$.

Raju & tom together can do a work in 10 day. In one day they will work $\frac{1}{10}$.

Tom & appu together can do it in 12 days. In one day they will work $\frac{1}{12}$.

Appu & raju together can do it in 15 days. In one day they will work $\frac{1}{15}$.

The one work is the half of the sum of work done by pairs of two  in one day.

$\frac{1}{2}(\frac{1}{10}+\frac{1}{12}+\frac{1}{15})=\frac{1}{t}$

$\frac{1}{10}+\frac{1}{12}+\frac{1}{15}=2(\frac{1}{t})$

$\frac{6+5+4}{60}=\frac{2}{t}$

$\frac{15}{60}=\frac{2}{t}$

$t=8$

Therefore, all the three will complete the work together in 8 days.