A borrowed Rs. 7000 from bank, after 3 years she Returned Rs. 3000 to the bank, After 5 years from starting she returned Rs. 5450 and settle her account. Find the rate of interest.

Answer

To solve the problem step by step, we need to determine the rate of interest based on the information given about the borrowed amount and the repayments made over time.

### Step 1: Understand the Borrowed Amount and Repayments
- A borrowed Rs. 7000 from the bank.
- After 3 years, A returned Rs. 3000.
- After a total of 5 years, A returned Rs. 5450 to settle the account.

### Step 2: Calculate the Remaining Amount After 3 Years
After 3 years, the amount left to be paid back is:
\[ \text{Remaining Amount} = \text{Initial Amount} - \text{Amount Returned} = 7000 - 3000 = 4000 \text{ Rs.} \]

### Step 3: Calculate the Total Amount Paid After 5 Years
After 5 years, A returned a total of Rs. 5450. This amount includes interest on the remaining Rs. 4000 for the additional 2 years.

### Step 4: Determine the Interest Paid Over 2 Years
The total amount paid after 5 years is Rs. 5450, which includes the remaining principal of Rs. 4000 plus interest for 2 years. Therefore, the interest paid over the 2 years is:
\[ \text{Interest} = \text{Total Amount Paid} - \text{Remaining Principal} = 5450 - 4000 = 1450 \text{ Rs.} \]

### Step 5: Calculate the Rate of Interest
The interest earned on the remaining principal of Rs. 4000 over 2 years is Rs. 1450. We can use the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (4000 Rs.)
- \( R \) = Rate of interest (unknown)
- \( T \) = Time (2 years)

Substituting the known values into the formula:
\[ 1450 = \frac{4000 \times R \times 2}{100} \]

### Step 6: Solve for R
Rearranging the equation to find R:
\[ 1450 = \frac{8000R}{100} \]
\[ 1450 = 80R \]
\[ R = \frac{1450}{80} = 18.125 \]

Thus, the rate of interest is:
\[ R = 18.125\% \]

### Final Answer
The rate of interest is **18.125%**.

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