₹ 6200 amounts to ₹ 9176 in 4 years at simple interest. If the interest rate is increased by 3% it would amount to how much?

### Concept & Incremental Simple Interest When the interest rate increases by a certain percentage, you do not need to calculate the original rate. You only need to calculate the *extra* interest generated by the *extra* rate and add it to the original total amount. $$\text{Extra Interest} = \frac{P \times \text{Increase in Rate} \times T}{100}$$ ### Step-by-Step Solution * Given Principal, $P = \text{₹ } 6200$ * Given Original Amount, $A_1 = \text{₹ } 9176$ * Given Time, $T = 4 \text{ years}$ * Given Rate Increase = $3\%$ p.a. * Calculate the Extra Interest generated by the $3\%$ increase: $\text{Extra } SI = \frac{6200 \times 3 \times 4}{100}$ $\text{Extra } SI = 62 \times 12 = \text{₹ } 744$ * Add the Extra Interest to the Original Amount to find the New Amount: $\text{New Amount} = 9176 + 744 = \text{₹ } 9920$ ### Exam Strategy & Shortcut Skip finding the original rate entirely. Multiply the rate increase by the years to get the total extra percentage ($3\% \times 4 = 12\%$). Then find $12\%$ of $6200$, which is $12 \times 62 = 744$. Add $744$ to $9176$ to get $9920$. ### Common Pitfall A massive time-waster is calculating the initial rate first ($SI = 2976 \rightarrow R = 12\%$), then adding $3\%$ to get $15\%$, and then recalculating the entire amount from scratch. ### Final Answer Therefore, the correct answer is **₹ 9920**.