Radha borrowed Rs. 3500 from bank and returned Rs. 1500 after 3 years. After 5 years from starting she returned Rs. 2725 and settle her account. What was the rate of interest ?

Answer

To solve the problem step by step, we need to calculate the rate of interest based on the information provided.

### Step 1: Understand the Borrowing and Repayment
Radha borrowed Rs. 3500 from the bank. After 3 years, she returned Rs. 1500.

**Calculation:**
- Amount borrowed = Rs. 3500
- Amount returned after 3 years = Rs. 1500
- Remaining amount after 3 years = Rs. 3500 - Rs. 1500 = Rs. 2000

**Hint:** Keep track of how much money is left after each repayment.

### Step 2: Determine the Total Amount Returned
After a total of 5 years, Radha returned Rs. 2725 to settle her account.

**Calculation:**
- Total amount returned after 5 years = Rs. 1500 (after 3 years) + Rs. 2725 (after 5 years) = Rs. 4225

**Hint:** Add the amounts returned to find the total repayment.

### Step 3: Calculate the Total Interest Paid
The total interest paid can be calculated by subtracting the principal amount from the total amount returned.

**Calculation:**
- Total interest paid = Total amount returned - Principal amount
- Total interest paid = Rs. 4225 - Rs. 3500 = Rs. 725

**Hint:** The interest is the extra amount paid over the principal.

### Step 4: Calculate the Interest for Each Period
The interest is calculated for two different periods:
1. For the first 3 years on Rs. 3500.
2. For the next 2 years on Rs. 2000 (remaining amount).

Let the rate of interest be R%.

**Calculation for the first 3 years:**
- Interest for first 3 years = (Principal × Rate × Time) / 100
- Interest for first 3 years = (3500 × R × 3) / 100

**Calculation for the next 2 years:**
- Interest for next 2 years = (Principal × Rate × Time) / 100
- Interest for next 2 years = (2000 × R × 2) / 100

### Step 5: Set Up the Equation
The total interest paid (Rs. 725) is the sum of the interest from both periods.

**Equation:**
\[ \frac{3500 \times R \times 3}{100} + \frac{2000 \times R \times 2}{100} = 725 \]

### Step 6: Simplify the Equation
Combine the terms in the equation:
\[ \frac{10500R + 4000R}{100} = 725 \]
\[ \frac{14500R}{100} = 725 \]

### Step 7: Solve for R
Multiply both sides by 100:
\[ 14500R = 72500 \]
Now, divide by 14500:
\[ R = \frac{72500}{14500} = 5 \]

### Conclusion
The rate of interest is **5%**.