Anil Sunil and Rajat can complete a work in 4 hours. If Anil does the work in 12 hour, Sunil in 10 hours . How long it take to Rajat to finish the alone

Given: 

Anil, Sunil, and Rajat can complete a work in 4 hours.

Anil does the work in 12 hours and Sunil in 10 hours.

To find: 

Here, we have to find how long will Rajat take to finish the work.

Solution:

We would consider total work to be 1.

Work done by Anil in one hour = $\frac{Total\ work}{Total\ number\ of\ hours\ taken}$

Work done by Anil in one hour $= \frac{1}{12}$.

Similarly,

Work done by Sunil in 1 hour$=\frac{1}{10}$

 Work done by Rajat in one hour be $\frac{1}{x}$.

Therefore,

Total work done by all three in one hour $= \frac{1}{12}\ +\ \frac{1}{10}\ +\ \frac{1}{x}$

Work done in one hour $\times$ Total number of hours $=$ Total work

$[\frac{1}{12}\ +\ \frac{1}{10}\ +\ \frac{1}{x}]\ \times\ 4\ =\ 1$

$\frac{1}{12}\ +\ \frac{1}{10}\ +\ \frac{1}{x}\ =\ \frac{1}{4}$

$\frac{1}{x}\ =\ \frac{1}{4}\ -\ \frac{1}{12}\ -\ \frac{1}{10}$

$\frac{1}{x} \ =\ \frac{1\times15\ -\ 1\times5\ -\ 1\times6}{60}$

$\frac{1}{x} \ =\ \frac{4}{60}$

$x=\frac{60}{4}$

$x=15$

$x = 15\ hours$

So, Rajat can complete the same work in 15 hours.

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Updated on: 10-Oct-2022

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