Introduction:
To determine the time required for the simple interest on a certain sum to be 0.225 times the principal at an interest rate of 10% per annum, we need to apply the formula for simple interest and solve for time. Simple interest is calculated using the formula:

Simple Interest = (Principal * Rate * Time) / 100

Given:
- Principal (P) = ?
- Rate (R) = 10% per annum = 10/100 = 0.10
- Simple Interest (SI) = 0.225 times the principal

Step 1: Understanding the Problem:
To solve the problem, we need to find the time (T) required for the simple interest to be 0.225 times the principal. Let's denote the principal as P and the time as T. We are given that the simple interest is 0.225 times the principal, so we can write the equation as:

SI = 0.225P

Step 2: Applying the Formula:
Substituting the values into the formula for simple interest, we have:

0.225P = (P * 0.10 * T) / 100

Simplifying the equation, we get:

0.225P = 0.001P * T

Step 3: Solving for Time:
To solve for time, we can cancel out the principal (P) on both sides of the equation. Dividing both sides by 0.001P, we have:

0.225 = T * 0.001

Now, we can isolate T by dividing both sides by 0.001:

T = 0.225 / 0.001

Simplifying the right-hand side of the equation, we get:

T = 225

Step 4: Interpretation:
The time required for the simple interest on a certain sum to be 0.225 times the principal at an interest rate of 10% per annum is 225 years.

Conclusion:
In this problem, we used the formula for simple interest to find the time required for the interest to be 0.225 times the principal. By substituting the given values into the formula and solving for time, we determined that it would take 225 years for the simple interest to reach 0.225 times the principal at a 10% per annum interest rate.