X started a work such that he can complete the whole work in 25 hours. After working for 20 hours, he worked with the rate such that the whole work can be completed in 50 hours. In how many hours X can complete the whole work?

Let's break down the problem step-by-step to find the total time taken by X to complete the work.

Step 1: Understand the initial rate of X
X can complete the entire work in 25 hours.
Therefore, the initial rate of work of X is:
$\mathrm{Initial\; Rate}=\frac{1}{25}\mathrm{of\; the\; work\; per\; hour}$

Step 2: Calculate the work completed in the first 20 hours
X works at his initial rate for 20 hours.
Work completed in 20 hours is:
$\mathrm{Work\; done}=20\times \frac{1}{25}=\frac{4}{5}\mathrm{of\; the\; work}$

Step 3: Calculate the remaining work
The total work is represented as 1 (or 100%).
The remaining work to be completed is:
$\mathrm{Remaining\; Work}=1-\frac{4}{5}=\frac{1}{5}\mathrm{of\; the\; work}$

Step 4: Find the new rate of X
After 20 hours, X changes his working speed to a rate such that the whole work would take 50 hours to complete if he worked at this rate from the beginning.
Therefore, the new rate of work of X is:
$\mathrm{New\; Rate}=\frac{1}{50}\mathrm{of\; the\; work\; per\; hour}$

Step 5: Calculate the time taken to complete the remaining work
Using the new rate, the time required to complete the remaining $\frac{1}{5}$ of the work is:
$\mathrm{Time\; taken\; for\; remaining\; work}=\frac{\mathrm{Remaining\; Work}}{\mathrm{New\; Rate}}=\frac{1/5}{1/50}=\frac{50}{5}=10\mathrm{hours}$

Step 6: Calculate the total time taken to complete the whole work
The total hours X worked is the sum of the time worked at the initial rate and the time worked at the new rate:
$\mathrm{Total\; Time}=20\mathrm{hours}+10\mathrm{hours}=30\mathrm{hours}$
Thus, X completes the whole work in 30 hours.