Question

X can do a piece of work in 25 days and Y can finish it in 20 days. They work together for 5 days and then X leaves. In how many days will Y finish the remaining work ?

Answer 1

Let the total work be $1$

Then, According to question X takes 25 days to do 1 work.

Then work done by X in 1 day=$\frac{1}{25}$

Also according to question Y takes 20 days to do 1 work.

Then work doe by Y in 1 day=$\frac{1}{20}$

Then total work done by both of them in 1 day $=\frac{1}{20}+\frac{1}{25}=\frac{9}{100}$

Then total work done by both of them 5 days$=\frac{45}{100}$

Then total work left $=1-\frac{45}{100}=\frac{55}{100}$

Now, As Y can do 1 work in 25 days therefore,

Y can do $\frac{55}{100}$ work in $\frac{55}{100}\times 25$ days

$=\frac{55}{4}$ days