A sum of money when invested for 5 years gives 5,250 as the amount. If the simple rate of interest was 2% per annum, more than what it was, the amount would have been 5600. The original sum invested was:

Options

A. 4000
B. 3250
C. 3750
D. 3500

Answer

To solve the problem step-by-step, we can follow these steps:

### Step 1: Understand the problem
We have an amount of ₹5,250 after 5 years at a simple interest rate of 2% per annum. If the interest rate were increased by 2%, the amount would be ₹5,600 after the same period.

### Step 2: Calculate the difference in amounts
The difference between the two amounts is:
\[ 5600 - 5250 = 350 \text{ rupees} \]

### Step 3: Find the difference in interest per year
Since this difference of ₹350 is the total interest earned over 5 years, we can find the interest earned per year:
\[ \text{Interest per year} = \frac{350}{5} = 70 \text{ rupees} \]

### Step 4: Relate the interest to the rate
The difference in interest of ₹70 corresponds to the increase in the interest rate of 2%. Thus, we can set up the following relationship:
\[ 2\% \text{ of Principal} = 70 \text{ rupees} \]

### Step 5: Calculate the Principal
To find the Principal (P), we can rearrange the equation:
\[ P = \frac{70 \times 100}{2} = 3500 \text{ rupees} \]

### Step 6: Conclusion
The original sum invested was ₹3,500.