The simple interest on a certain sum of money for 5 years at 10% p.a. is ₹880 more than the simple interest on the same sum at 7% p.a. for 4 years. Find the sum.

Let's denote the sum of money as \( P \).

### Step 1: Simple Interest Formula
The formula for simple interest is:
\[
\text{Simple Interest (SI)} = \frac{P \times R \times T}{100}
\]
Where:
- \( P \) is the principal (the sum we need to find),
- \( R \) is the rate of interest,
- \( T \) is the time in years.

### Step 2: Simple Interest for the two cases
We have two scenarios:
1. **First case:** 
   - Rate = 10%,
   - Time = 5 years,
   - Interest = \( \frac{P \times 10 \times 5}{100} = \frac{50P}{100} = \frac{P}{2} \).

2. **Second case:**
   - Rate = 7%,
   - Time = 4 years,
   - Interest = \( \frac{P \times 7 \times 4}{100} = \frac{28P}{100} = \frac{7P}{25} \).

### Step 3: Condition Given in the Problem
According to the problem, the simple interest in the first case is ₹880 more than in the second case:
\[
\frac{P}{2} - \frac{7P}{25} = 880
\]

### Step 4: Solving the Equation
To solve this, we first find a common denominator for the terms on the left side:
\[
\frac{P}{2} - \frac{7P}{25} = \frac{25P - 14P}{50} = \frac{11P}{50}
\]
Now, equate this to 880:
\[
\frac{11P}{50} = 880
\]

Multiply both sides by 50:
\[
11P = 880 \times 50
\]
\[
11P = 44000
\]

Finally, divide by 11 to find \( P \):
\[
P = \frac{44000}{11} = 4000
\]

### Conclusion:
The sum of money is ₹4000.

Would you like further details or have any questions?

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Here are 5 related questions to extend your understanding:

1. How would the problem change if the interest rate in the second case was 8% instead of 7%?
2. What would happen if the time in the second case was increased by 1 year?
3. How can you use the formula for compound interest to solve similar problems?
4. What would be the difference if the interest was compounded annually instead of using simple interest?
5. How can this method be applied to find the interest difference over shorter time periods?

**Tip:** When solving for unknowns in interest-related problems, always ensure you're clear about which interest formula to use: simple or compound.

Learn how to find the sum of money when the simple interest for 5 years at 10% p.a. is ₹880 more than the simple interest for 4 years at 7% p.a. This problem uses the simple interest formula and involves solving linear equations. Suitable for students in Grades 8-10.

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