A sum of money at simple interest amounts to Rs 800 in 2 years and to Rs 1200 in 6 years. The sum is……………

Options

A. Rs 600
B. Rs 1000
C. Rs 400
D. Rs 500

Explanation

To solve the problem step by step, we need to find the principal amount given that a sum of money at simple interest amounts to Rs 800 in 2 years and Rs 1200 in 6 years.

### Step 1: Understand the given information
We know:
- Amount after 2 years (A1) = Rs 800
- Amount after 6 years (A2) = Rs 1200

### Step 2: Calculate the simple interest for the period between 2 years and 6 years
To find the simple interest earned from year 2 to year 6, we subtract the amount after 2 years from the amount after 6 years:
\[ \text{Simple Interest for 4 years} = A2 - A1 = 1200 - 800 = Rs 400 \]

### Step 3: Calculate the simple interest for 1 year
Since the interest of Rs 400 is for 4 years, we can find the interest for 1 year by dividing the total interest by the number of years:
\[ \text{Simple Interest for 1 year} = \frac{400}{4} = Rs 100 \]

### Step 4: Calculate the simple interest for 2 years
Now, we can calculate the simple interest for 2 years:
\[ \text{Simple Interest for 2 years} = 100 \times 2 = Rs 200 \]

### Step 5: Calculate the principal amount
The principal amount can be calculated by subtracting the simple interest for 2 years from the amount after 2 years:
\[ \text{Principal} = A1 - \text{Simple Interest for 2 years} = 800 - 200 = Rs 600 \]

### Conclusion
The sum of money (principal) is Rs 600.

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