X require 5 days more to complete a work than Y. After starting a work for 4 days Y left the job and X completed the remaining work in 5 days. Please find out how many days they will reqiuer to complete the work individually.

Let's call t_x the time required for person X to complete the job and t_y the time require for person Y to complete the job.

Since we know that it requires person X and extra 5 days to complete it, we have:

(1) t_x = t_y + 5.

Now, let's also call x the rate at which person X works and y the rate at which person Y works.

The time required for each person to finish the job is the reciprocal of their rate. (In other words, if a person can do \frac{1}{3} of the job each day, it will take 3 days to complete the job).

(2) t_x=\frac{1}{x}
(3) t_y=\frac{1}{y}

Finally, we know that the job required 4 days of work from Y followed by 5 additional days from X.

(4) 4y+5x=1.

The 1 on the right hand side of the equation represents 100% of the job completed. In other words, 4 days of work at Y's rate + 5 days of work at X's rate resulted in 100% of the job being finished.

Now it's simply a matter of solving equations (1) and (4) simulataneously to find x and y, then plugging into (2) and (3) to find the times required for each individually.

For what it's worth, I come up with

t_y=\frac{10}{\sqrt{6}-1} or about 6.9 days, and
t_x=\frac{10}{\sqrt{6}-1}+5 or about 11.9 days.