An amount earns a total simple interest of Rs 3200 at the rate of 6.25 percent per annum in 4 years. What is the principal amount in rupees?

Introduction / Context:
This question is a direct application of the simple interest formula to find the principal when the interest earned, rate, and time are known. The rate is given in decimal form as 6.25 percent per annum, and the total simple interest over 4 years is specified. The task is to work backwards to find the original amount invested.

Given Data / Assumptions:
- Simple interest SI = Rs 3200.
- Rate of interest R = 6.25 percent per annum.
- Time T = 4 years.
- We must find the principal P.

Concept / Approach:
The basic simple interest formula is:
SI = (P * R * T) / 100We know SI, R, and T, so we rearrange this formula to solve for P:
P = (SI * 100) / (R * T)We substitute the given values and compute P. The decimal rate 6.25 percent must be handled carefully in the arithmetic.

Step-by-Step Solution:
Given SI = 3200, R = 6.25, T = 4.Use P = (SI * 100) / (R * T).Compute denominator R * T = 6.25 * 4 = 25.Compute numerator SI * 100 = 3200 * 100 = 320000.So, P = 320000 / 25.Compute P: 320000 / 25 = 12800.Therefore, the principal amount is Rs 12800.

Verification / Alternative check:
We can verify by plugging P = 12800 back into the simple interest formula. SI = (12800 * 6.25 * 4) / 100. First, 6.25 * 4 = 25. Then, SI = (12800 * 25) / 100. Compute 12800 * 25 = 320000. Divide by 100 to get 3200, which matches the given simple interest. This confirms that P = 12800 is correct.

Why Other Options Are Wrong:
If P were Rs 13800, the simple interest would be (13800 * 6.25 * 4) / 100 = 3450, not 3200. For Rs 11800, the interest would be 2950. For Rs 14800, the interest would be 3700. For Rs 16000, the interest would be 4000. None of these match the given SI of 3200. Only Rs 12800 produces the specified simple interest with the given rate and time.

Common Pitfalls:
Common mistakes include miscalculating 6.25 * 4, forgetting to divide by 100, or incorrectly handling the decimal rate. Some students also confuse 6.25 percent with 6.25 as a simple multiplier, which is wrong. Always use the formula SI = (P * R * T) / 100 and double check intermediate multiplications to avoid arithmetic errors.

Final Answer:
The principal amount is Rs 12800.