Let the principal amount (sum) be $P$.

Step 1: Calculating Simple Interest for 15 months at 7.5% per annum

The formula for simple interest (SI) is: $\text{SI} = \frac{P \times R \times T}{100}$ where:

• $P$ is the principal,
• $R$ is the rate of interest per annum,
• $T$ is the time in years.

For the first case:

• $R = 7.5\%$,
• $T = \frac{15}{12}$ years (since 15 months is 1.25 years).

Substituting values: $\text{SI}_1 = \frac{P \times 7.5 \times 1.25}{100} = \frac{9.375P}{100} = 0.09375P$

Step 2: Calculating Simple Interest for 8 months at 12.5% per annum

For the second case:

• $R = 12.5\%$,
• $T = \frac{8}{12}$ years (since 8 months is $\frac{2}{3}$ years).

Substituting values: $\text{SI}_2 = \frac{P \times 12.5 \times \frac{2}{3}}{100} = \frac{25P}{300} = 0.08333P$

Step 3: Setting up the equation

According to the problem, the difference in simple interest between the two cases is Rs. 32.50: $0.09375P - 0.08333P = 32.50$ Simplifying the left side: $0.01042P = 32.50$

Step 4: Solving for $P$

$P = \frac{32.50}{0.01042} = 3120$

Answer

The sum is Rs. 3120.

Would you like further explanation or have additional questions?

Here are related questions to explore further:

1. How is simple interest affected by changes in the rate and time?
2. What would be the effect if the time period in the second case was doubled?
3. How does compound interest differ from simple interest in such cases?
4. How can interest be calculated for different compounding periods within a year?
5. What are common practical applications of simple interest in real-life scenarios?

Tip: When dealing with months in interest calculations, always convert them to years for accurate results.