The simple interest on a certain sum of 3 years at 8% per annum is ₹96 more than the simple interest on the same sum for 2 years at 9% annum. Find the sum

Answer

To solve the problem, we need to find the sum (principal amount) based on the information given about simple interest. Let's denote the principal amount as \( P \).

### Step-by-Step Solution:

1. **Understand the formula for Simple Interest (SI)**:
The formula for calculating simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Calculate the Simple Interest for 3 years at 8%**:
For the first part of the problem, we calculate the simple interest for 3 years at 8%:
\[ SI_1 = \frac{P \times 8 \times 3}{100} = \frac{24P}{100} = 0.24P \]

3. **Calculate the Simple Interest for 2 years at 9%**:
For the second part of the problem, we calculate the simple interest for 2 years at 9%:
\[ SI_2 = \frac{P \times 9 \times 2}{100} = \frac{18P}{100} = 0.18P \]

4. **Set up the equation based on the given information**:
According to the problem, the simple interest for 3 years at 8% is ₹96 more than the simple interest for 2 years at 9%. Therefore, we can set up the equation:
\[ SI_1 = SI_2 + 96 \]
Substituting the values we calculated:
\[ 0.24P = 0.18P + 96 \]

5. **Solve for \( P \)**:
To isolate \( P \), we subtract \( 0.18P \) from both sides:
\[ 0.24P - 0.18P = 96 \]
This simplifies to:
\[ 0.06P = 96 \]
Now, divide both sides by \( 0.06 \):
\[ P = \frac{96}{0.06} = 1600 \]

6. **Conclusion**:
The principal amount (sum) is ₹1600.