Ronika deposited Rs 7,000 at simple interest and the amount grew to Rs 9,200 after 3 years. If the rate of interest had been 2% per annum higher than the actual rate, what amount would she have received after the same period of 3 years?

Introduction / Context:
This question asks you to first determine the actual simple interest rate from the original deposit and amount, and then consider what would happen if the rate were 2% higher. It is an excellent example of how to adjust an existing simple interest scenario when the rate changes, without altering the principal or time.

Given Data / Assumptions:

Principal P = Rs 7,000.
Amount after 3 years, A_original = Rs 9,200.
Time T = 3 years.
Rate of interest per annum is r% initially, then (r + 2)% in the hypothetical case.
Simple interest SI = A - P, and SI = (P * r * T) / 100.

Concept / Approach:
First, we compute the simple interest earned in 3 years using the original data, then find the rate r. Once we know r, we increase it by 2% to obtain the new rate. Using this new rate, we calculate the new simple interest for 3 years on the same principal and add it to the principal to get the revised amount Ronika would have received.

Step-by-Step Solution:
Step 1: Compute original simple interest: SI_original = A_original - P = 9200 - 7000 = 2200. Step 2: Use SI = (P * r * T) / 100 with SI_original = 2200, P = 7000, T = 3. Step 3: 2200 = (7000 * r * 3) / 100. Step 4: Multiply both sides by 100: 220000 = 21000r. Step 5: Therefore, r = 220000 / 21000. Step 6: Simplify r = 220000 / 21000 = 220 / 21 ≈ 10.47619%. Step 7: The increased rate is r_new = r + 2 ≈ 12.47619%. Step 8: Instead of working with decimals, note that extra interest due to the extra 2% over 3 years is (P * 2 * 3) / 100. Step 9: Extra SI = (7000 * 2 * 3) / 100 = (7000 * 6) / 100 = 420. Step 10: New total interest = SI_original + extra SI = 2200 + 420 = 2620. Step 11: New amount A_new = P + new total interest = 7000 + 2620 = 9620.

Verification / Alternative check:
You can also compute the interest directly at the increased rate. At r_new ≈ 12.47619%, SI_new = (7000 * r_new * 3) / 100, which numerically equals 2620 when computed precisely. Adding to principal 7000 gives 9620, consistent with the stepwise method that separates original and extra interest.

Why Other Options Are Wrong:
Amounts such as Rs 9,500, Rs 9,760, or Rs 9,700 result from miscalculating the rate or the extra interest. Rs 9,850 is too large for an increase of only 2% in the rate over 3 years. Only Rs 9,620 correctly represents principal plus the higher total interest.

Common Pitfalls:
Many students recompute the entire rate numerically and approximate too early, leading to rounding errors. A cleaner approach is to separate the original interest and the extra interest due to the 2% increase. Always focus on the extra interest as P * extra_rate * time / 100, then add it to the original amount.

Final Answer:
If the rate had been 2% higher, Ronika would have received Rs 9,620 after 3 years.