At simple interest rate, an amount becomes Rs. 1120 in 4 yeas and Rs. 1200 in 5 years. Principal amount is:

Question

Accepted Answer

To determine the principal amount using the given information, we need to understand how simple interest works. Simple interest is calculated using the formula:

$$ \text{Simple Interest (SI)} = \frac{\text{Principal (P)} \times \text{Rate (R)} \times \text{Time (T)}}{100} $$

From the problem, we know:

1. The amount becomes Rs. 1120 in 4 years.
2. The amount becomes Rs. 1200 in 5 years.

The difference in the amounts over the 1-year period (from year 4 to year 5) is Rs. 1200 - Rs. 1120 = Rs. 80. This Rs. 80 is the simple interest earned in one year.

Since simple interest is the same each year, the annual interest is Rs. 80. Therefore, for 4 years, the total interest is Rs. 80 $\times$ 4 = Rs. 320.

Now, we can find the principal amount by subtracting the total interest for 4 years from the amount at the end of 4 years:

$$ \text{Principal (P)} = \text{Amount after 4 years} - \text{Total Interest for 4 years} $$
$$ \text{Principal (P)} = 1120 - 320 = 800 $$

Thus, the principal amount is Rs. 800, which corresponds to Option 1.

**Explanation for why other options are incorrect:**

- **Option 2 (Rs. 1000):** If the principal were Rs. 1000, the interest for 4 years would be calculated as Rs. 1000 $\times$ R $\times$ 4/100. However, given the interest for 4 years is Rs. 320, this would not match the calculation if the principal were Rs. 1000.

- **Option 3 (Rs. 1050):** Similarly, if the principal were Rs. 1050, the interest for 4 years would not match the Rs. 320 calculated from the given amounts. The mismatch in interest calculation confirms this option is incorrect.

- **Option 4 (Rs. 1080):** If the principal were Rs. 1080, the interest for 4 years would also not align with the Rs. 320 interest derived from the problem statement. This discrepancy confirms that this option is incorrect.

Therefore, based on the calculations and logical reasoning, Option 1 (Rs. 800) is the correct answer.