Question

anil and raju can work together to finish a work in 10 days. they together work on it for 2 days and then raju leaves. the rest of the work was done by anil alone in 30 days. in how much time can raju do the work alone?

Answer 1

38 days


Hope it is right

Answer 2

Given:

Anil and Raju can finish the work together in 10 days

They work together for 2 days

Raju leaves after 2 days and Anil does the rest of the work alone in 30 days

To find:

The time in which Raju can do the work alone

Solution:

In 1 day, the amount of work done by Anil and Raju together = $\frac{1}{10}$

Anil and Raju have worked together for 2 days

∴ In 2 days, the amount of work done By Anil and Raju together = $\frac{2}{10} = \frac{1}{5}$

∴ Remaining work to be done = $1 - \frac{1}{5} = \frac{5 - 1}{5} = \frac{4}{5}$ ← amount of work done by Anil alone in 30 days

So,

If $\frac{4}{5}$th of the work is done in 30 days

Then, the complete work will be done by Anil in = $30 * \frac{5}{4} = \frac{150}{4} = \frac{75}{2} days$

Now,

The amount of work by Raju alone in 1 day is,

= [Amount of work done by Raju and Anil in 1 day] - [Amount of work done by Anil in 1 day]

$= \frac{1}{10}\: -\: \frac{2}{75}\\ \\\\= \frac{15\: -\: 4}{150}\\\\\\= \frac{11}{150}$

Thus, Raju can do the work alone in $\frac{150}{11} \:days \:or\:13.63\:days$.

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