Simple Interest — ₹ 4200 amounts to ₹ 5712 in 4 years. If the rate is then increased by 3 percentage points, what will be the new amount after the same 4 years on ₹ 4200?

Introduction / Context:
This problem first determines the original rate using a known amount after 4 years, then increases the rate by 3 percentage points to compute a new amount for the same principal and time.

Given Data / Assumptions:

• Original principal P = ₹ 4200.
• Original amount A = ₹ 5712 after t = 4 years.
• Rate is increased by 3 percentage points (e.g., 9% to 12%).

Concept / Approach:
Simple interest: A = P * (1 + r * t). First solve for the original rate r from the first scenario, then compute the new amount with r_new = r + 0.03.

Step-by-Step Solution:
Original: 5712 = 4200 * (1 + r * 4).Divide: 5712 / 4200 = 1 + 4r.5712 / 4200 = 1.36; hence 4r = 0.36 ⇒ r = 0.09 = 9%.Increase rate by 3 points ⇒ r_new = 12% = 0.12.New amount = 4200 * (1 + 0.12 * 4) = 4200 * 1.48 = ₹ 6216.

Verification / Alternative check:
Compute SI directly: new SI = 4200 * 0.12 * 4 = 4200 * 0.48 = 2016; Amount = 4200 + 2016 = 6216.

Why Other Options Are Wrong:
₹ 6372 is too high; ₹ 6120 too low; ₹ 4000 or ₹ 3000 ignore interest.

Common Pitfalls:
Confusing “+3%” (relative increase) with “+3 percentage points.” Here it is absolute points, so 9% becomes 12%.

Final Answer:
₹ 6216