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?

Hint: Find the work done by X and Y in one day. Thus find their work done in 5 days. To get the remaining work done by Y, subtract the work done by (X + Y) in 5 days from one. Thus find the number of days Y will take to finish the work.

It is said that X can do work in 25 days.

So, the work done by X in one day $={}^{1}/{}_{25}$ .

Similarly, Y can do work in 20 days.

So, the work done by Y in one day $={}^{1}/{}_{20}$.

Now let us find the work done together by X and Y in one day.

$X+Y={}^{1}/{}_{25}+{}^{1}/{}_{20}$.

Thus the work done by (X + Y) in one day $=\dfrac{1}{25}+\dfrac{1}{20}$.

So, the work done by (X + Y) in 5 days $=5\times \left( \dfrac{1}{25}+\dfrac{1}{20} \right)$

$=\dfrac{5}{25}+\dfrac{5}{20}=\dfrac{1}{5}+\dfrac{1}{4}=\dfrac{4+5}{5\times 4}={}^{9}/{}_{20}$.

Thus the work done by (X + Y) in 5 days $={}^{9}/{}_{20}$.

It is said that X leaves after 5 days of work. So Y has to finish the remaining work.

Thus the remaining work $=1-{}^{9}/{}_{20}=\dfrac{20-9}{20}={}^{11}/{}_{20}$.

Let us find in how many days can Y complete the remaining work$=\dfrac{Remaining\text{ }work}{Work\text{ }done\text{ }by\text{ }Y\text{ }in\text{ }1\text{ }day}=\dfrac{{}^{11}/{}_{20}}{{}^{1}/{}_{20}}=11$.

Thus Y can finish the remaining work in 11 days.

Note: After getting the work of 5 days, subtract it from 1 to get the remaining work. Remember to find the remaining work done by Y and how many days it took Y to complete the same.