A sum of Rs 1,200 amounts to Rs 1,740 in 3 years at simple interest. If the annual rate of interest is increased by 3 percentage points, what will be the new amount, in rupees, after 3 years on the same principal?

Introduction / Context:
This question focuses on determining an unknown simple interest rate from one scenario and then applying an increased rate to find a new maturity amount. It reflects real life situations where a bank or financial institution changes its interest rates, and an investor wants to know how this affects the amount accumulated over the same period on the same principal.

Given Data / Assumptions:

Original principal P = Rs 1,200
Original amount after 3 years = Rs 1,740
Original time T = 3 years
Interest is simple interest in both scenarios
New rate is 3 percentage points higher than the original rate

Concept / Approach:
First, deduce the original annual simple interest rate from the initial information. The interest earned is the difference between the amount and the principal. Then use I = P * r * T to solve for r. Once r is known, increase it by 3 percentage points to get the new rate r_new. Finally, compute the new simple interest for 3 years at this new rate and add it to the principal to get the new maturity amount.

Step-by-Step Solution:
Step 1: Find the original simple interest over 3 years. I_original = amount - principal = 1,740 - 1,200 = 540 rupees. Step 2: Use the simple interest formula I = P * r * T to get r. 540 = 1,200 * r * 3. Step 3: Solve for r: r = 540 / (1,200 * 3). Denominator = 1,200 * 3 = 3,600. r = 540 / 3,600 = 0.15 = 15 percent per annum. Step 4: Increase the rate by 3 percentage points. New rate r_new = 15 percent + 3 percent = 18 percent per annum. Step 5: Compute new interest with r_new for 3 years. I_new = 1,200 * 0.18 * 3. Step 6: Evaluate: 1,200 * 0.18 = 216 per year; over 3 years I_new = 216 * 3 = 648. Step 7: Find the new amount after 3 years. New amount = principal + I_new = 1,200 + 648 = 1,848 rupees.

Verification / Alternative check:
An alternative reasoning is to observe that the original rate 15 percent gives 180 rupees interest per year (since 1,200 * 0.15 = 180). When the rate increases to 18 percent, the annual interest becomes 1,200 * 0.18 = 216 rupees, which is 36 rupees more per year. Over 3 years, the extra interest due to the rate increase is 36 * 3 = 108 rupees. The original interest was 540 rupees, so the new interest is 540 + 108 = 648 rupees. Adding this to the principal again gives 1,848 rupees, confirming the result.

Why Other Options Are Wrong:
Option Rs 1,946 would require a higher rate than 18 percent per year over 3 years. Option Rs 1,812 and option Rs 1,924 correspond to different combinations of rate and time and do not match the specified 3 percent increase from 15 percent. Only Rs 1,848 is consistent with 18 percent simple interest on 1,200 rupees over 3 years.

Common Pitfalls:
A common mistake is to add 3 percent of the original amount instead of increasing the rate itself by 3 percentage points. Another error is miscalculating the original rate or using 3 years twice. Candidates may also confuse percentage points with relative percentage change. It is crucial to first compute the original rate accurately using I = P * r * T, then add 3 percentage points directly to that rate before recomputing the future amount.

Final Answer:
The new amount after 3 years at the higher rate is Rs 1,848.