Equalize simple interests — find the time: Simple interest on ₹ 1680 for 4 years at 7.5% per annum equals the simple interest on ₹ 1200 at 7% per annum for some time T. Find T.

Introduction / Context:
When two simple interests are equal, set their expressions equal and solve for the unknown time. This is a direct proportion problem linking principal, rate, and time.

Given Data / Assumptions:

• I1: P1 = ₹ 1680, r1 = 7.5% p.a., t1 = 4 years
• I2: P2 = ₹ 1200, r2 = 7% p.a., t2 = T (unknown)

Concept / Approach:
Equalize simple interests: (P1 * r1 * t1)/100 = (P2 * r2 * T)/100 → P1 * r1 * t1 = P2 * r2 * T → solve for T.

Step-by-Step Solution:
I1 = 1680 * 7.5% * 4 = 1680 * 0.075 * 4 = ₹ 504Set I2 equal: 1200 * 7% * T = 5041200 * 0.07 * T = 504 → 84 * T = 504 → T = 6 years

Verification / Alternative check:
Compute I2 with T = 6: 1200 * 0.07 * 6 = ₹ 504 (matches I1).

Why Other Options Are Wrong:
Any value other than 6 fails to produce ₹ 504 for I2.

Common Pitfalls:
Dropping the /100 factor or mismultiplying rates given as fractions or percentages.

Final Answer:
6 years