Manu invested Rs 14,800 at 7% per annum simple interest. After how many years will she earn a simple interest of Rs 15,800 on this amount?

Introduction / Context:
This question involves determining the time required for a specified amount of simple interest to accumulate on a given principal at a fixed rate. The interest amount is even larger than the principal, so the time period will be relatively long. The problem tests your ability to rearrange the simple interest formula to solve for time when principal, rate, and total interest are known.

Given Data / Assumptions:
- Principal P = Rs 14,800. - Rate of interest R = 7% per annum. - Required simple interest I = Rs 15,800. - Simple interest is applied uniformly over time. - We must find the time T in years.

Concept / Approach:
The simple interest formula is I = P * R * T / 100. Here P and R are given, and I is the interest we want to reach. We rearrange the formula to solve for T as T = I * 100 / (P * R). After substituting the given values, we perform the arithmetic carefully to obtain T in decimal years, which we can express in the given options. Because the interest is greater than the principal, we expect the time to exceed roughly 14 years (since at 7% per year, 14 years would produce interest close to the principal).

Step-by-Step Solution:
Step 1: Start with I = P * R * T / 100. Step 2: Rearrange to solve for T: T = I * 100 / (P * R). Step 3: Substitute I = 15,800, P = 14,800, R = 7. Step 4: T = 15,800 * 100 / (14,800 * 7). Step 5: Compute the denominator: 14,800 * 7 = 103,600. Step 6: Compute the numerator: 15,800 * 100 = 1,580,000. Step 7: So T = 1,580,000 / 103,600. Step 8: Divide to obtain T ≈ 15.250965 years. Step 9: Rounded appropriately, T ≈ 15.25 years. Step 10: Therefore, Manu will obtain Rs 15,800 as simple interest in approximately 15.25 years.

Verification / Alternative check:
We can check by computing interest for 15.25 years: I = 14,800 * 7 * 15.25 / 100. First 7 * 15.25 = 106.75. Then I = 14,800 * 106.75 / 100 = 14,800 * 1.0675. Multiplying gives I approximately 15,800, matching the required interest. This confirms that 15.25 years is consistent with the given data.

Why Other Options Are Wrong:
Shorter times such as 13.5 years or 14 years would generate less interest than Rs 15,800, because there would be fewer years for interest to accumulate. A time of 16.75 or 18 years would produce more interest than required. Only about 15.25 years gives interest of Rs 15,800 exactly under the given principal and rate, so the other options are inconsistent with the formula.

Common Pitfalls:
A frequent error is to mistakenly use amount instead of interest in the formula, or to misplace the factor 100 in the numerator or denominator when solving for T. Others may round too early, leading to slight discrepancies in the final answer. Keeping the full fraction until the end and then rounding to two decimal places helps preserve accuracy and match the given options precisely.

Final Answer:
Manu will obtain Rs 15,800 as simple interest after approximately 15.25 years.