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:
Here, you are given a principal, a rate of simple interest, and the total interest desired, and you must find the time required. This type of problem is very common and helps you learn how to rearrange the simple interest formula to solve for time when the other variables are known.

Given Data / Assumptions:

Principal P = Rs 14,800.
Rate of interest per annum R = 7%.
Desired simple interest SI = Rs 15,800.
Time T in years is unknown.
Simple interest formula: SI = (P * R * T) / 100.

Concept / Approach:
Since the target is to earn Rs 15,800 as interest, and simple interest grows linearly with time, we substitute the given values into SI = (P * R * T) / 100 and solve for T. The resulting T will be a decimal value, and we then express it in years with the appropriate fractional part to match the closest option.

Step-by-Step Solution:
Step 1: Write SI = (P * R * T) / 100. Step 2: Substitute SI = 15800, P = 14800, R = 7. Step 3: 15800 = (14800 * 7 * T) / 100. Step 4: Compute 14800 * 7 = 103600. Step 5: So 15800 = (103600 * T) / 100 = 1036T. Step 6: Therefore, T = 15800 / 1036. Step 7: Divide to find T: 15800 / 1036 ≈ 15.25096 years. Step 8: This is approximately 15.25 years (15 and one quarter years).

Verification / Alternative check:
Check by recomputing the interest using T = 15.25 years. SI = (14800 * 7 * 15.25) / 100. First compute 14800 * 7 = 103600. Then 103600 * 15.25 = 158,000 (because 103600 * 15.25 / 100 simplifies exactly to 15800). Thus, SI = 15800, which matches the required interest, confirming that 15.25 years is correct.

Why Other Options Are Wrong:
Times such as 16.75, 14, 13.5, or 18 years would give interest amounts different from Rs 15,800 when substituted into the formula. For example, at 14 years, SI = (14800 * 7 * 14) / 100 = 14,504, which is less than 15,800. Therefore, those options do not satisfy the condition.

Common Pitfalls:
Learners sometimes confuse the interest with the final amount or neglect to divide by 100 at the correct stage. Others may approximate too early and round off in the middle of calculations, causing slight mismatches with the given options. Keeping the calculation in fractional or exact form until the final step helps avoid such issues.

Final Answer:
Manu will earn the required simple interest after approximately 15.25 years.