A sum invested on simple interest grows to Rs 22500/- and Rs 25500/- is seven and nine years respectively. What is the rate percentage of the interest ?

To solve this problem, we need to use the formula for simple interest which is I = PRT/100, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years.

1. First, we need to find out the principal amount. We know that the sum grows to Rs 22500 in 7 years and Rs 25500 in 9 years. So, the interest for 2 years is Rs 25500 - Rs 22500 = Rs 3000.

2. Now, we can use the simple interest formula to find the rate of interest. We know that the interest for 2 years is Rs 3000, so we can write the equation as 3000 = PR2/100.

3. We also know that the principal amount is Rs 22500 - 7 years interest. But we don't know the 7 years interest yet. However, we know that the 2 years interest is Rs 3000, so the 7 years interest would be 7/2 * Rs 3000 = Rs 10500.

4. Now we can find the principal amount which is Rs 22500 - Rs 10500 = Rs 12000.

5. Now we can substitute P = Rs 12000 and I = Rs 3000 in the simple interest formula and solve for R. The equation becomes 3000 = 12000R2/100. Solving for R, we get R = 12.5%.

So, the rate of interest is 12.5%.