If the simple interest on a certain sum at 4% per annum for 4 years is Rs. 80 more than the interest on the same sum for 3 years at 5% per annum, find the sum.

Answer

To solve the problem, we need to use the formula for Simple Interest (SI), which is given by:

\[ SI = \frac{P \times R \times T}{100} \]

where:
- \( P \) = Principal amount (the sum we need to find)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 1: Calculate the Simple Interest at 4% for 4 years

Using the formula for Simple Interest, we can express the interest for 4 years at 4% as:

\[ SI_1 = \frac{P \times 4 \times 4}{100} = \frac{16P}{100} = 0.16P \]

### Step 2: Calculate the Simple Interest at 5% for 3 years

Next, we calculate the interest for 3 years at 5%:

\[ SI_2 = \frac{P \times 5 \times 3}{100} = \frac{15P}{100} = 0.15P \]

### Step 3: Set up the equation based on the problem statement

According to the problem, the interest at 4% for 4 years is Rs. 80 more than the interest at 5% for 3 years. Therefore, we can set up the equation:

\[ SI_1 = SI_2 + 80 \]

Substituting the values we calculated:

\[ 0.16P = 0.15P + 80 \]

### Step 4: Solve for \( P \)

Now, we will solve for \( P \):

1. Subtract \( 0.15P \) from both sides:

\[ 0.16P - 0.15P = 80 \]

2. This simplifies to:

\[ 0.01P = 80 \]

3. Now, divide both sides by 0.01:

\[ P = \frac{80}{0.01} = 8000 \]

### Conclusion

The principal amount (the sum) is Rs. 8000.

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