A sum of money at simple interest amounts to Rs.8150 in 3 years and to Rs.8540 in 4 The sum is:

Options

A. Rs.7,000
B. Rs.6,900
C. Rs.6,500
D. Rs.6,980

Answer

To solve the problem step by step, we need to find the principal sum of money given the amounts after 3 years and 4 years at simple interest.

### Step 1: Identify the amounts after 3 years and 4 years
- Amount after 3 years (A3) = Rs. 8150
- Amount after 4 years (A4) = Rs. 8540

### Step 2: Calculate the interest for 1 year
The interest for the 4th year can be calculated by subtracting the amount after 3 years from the amount after 4 years:
- Interest for 1 year (I) = A4 - A3
- I = 8540 - 8150
- I = Rs. 390

### Step 3: Calculate the total interest for 3 years
Now that we know the interest for 1 year, we can calculate the total interest for 3 years:
- Total Interest for 3 years (I_total) = 3 * I
- I_total = 3 * 390
- I_total = Rs. 1170

### Step 4: Set up the equation for the total amount after 3 years
The amount after 3 years can be expressed as the sum of the principal (P) and the total interest for 3 years:
- A3 = P + I_total
- 8150 = P + 1170

### Step 5: Solve for the principal (P)
Now, we can rearrange the equation to find the principal:
- P = 8150 - 1170
- P = Rs. 6980

### Conclusion
The sum of money (the principal) is Rs. 6980.