Question

mohan can do a piece of work in 10 days and ramesh can do the same work in 15 days if suresh who can finish the same work in 30 days joins them then how long will three of them together take to complete the work​

Answer 1

Given:

Mohan can do a piece of work in 10 days and Ramesh can do the same work in 15 days

If Suresh who can finish the same work in 30 days joins them

To find:

How long will three of them together take to complete the work​?

Solution:

Mohan can do a piece of work in 10 days

Then, in 1 day, work completed by Mohan = $\frac{1}{10}$

Ramesh can do the same piece of work in 15 days

Then, in 1 day, work completed by Ramesh = $\frac{1}{15}$

Suresh can do the same work in 30 days

Then, in 1 day, work completed by Suresh = $\frac{1}{30}$

Now,

In 1 day, work completed by 3 of them together is,

= $\frac{1}{10} + \frac{1}{15} + \frac{1}{30}$

taking L.C.M of the denominators

= $\frac{3+2+1}{30}$

= $\frac{6}{30}$

= $\frac{1}{5}$

Thus, the 3 of them will together take 5 days to complete the work.

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