The difference between the simple interest on a sum of money for \(3\frac{1}{2}\) years at the rate of 12% per annum and simple interest on the same sum of money for \(4\frac{1}{2}\) years at 10% per annum is ₹360 . Find the sum(in ₹).

Question

Question

This question was previously asked in

SSC Selection Post 2024 (Higher Secondary Level) Official Paper (Held On: 21 Jun, 2024 Shift 2)

Answer 1

Given:

Simple interest for \(3\frac{1}{2}\) years at 12% per annum.

Simple interest for \(4\frac{1}{2}\) years at 10% per annum.

Difference in simple interest = ₹360.

Formula Used:

Simple Interest (SI) = (Principal (P) × Rate (R) × Time (T)) / 100

Calculation:

Let the sum be P.

SI for \(3\frac{1}{2}\) years at 12% per annum:

SI₁ = (P × 12 × 7/2) / 100

SI₁ = (P × 42) / 100

SI for 4½ years at 10% per annum:

SI₂ = (P × 10 × 9/2) / 100

SI₂ = (P × 45) / 100

Difference between the two simple interests:

SI₂ - SI₁ = ₹360

(P × 45) / 100 - (P × 42) / 100 = 360

(45P - 42P) / 100 = 360

3P / 100 = 360

3P = 360 × 100

3P = 36000

P = 36000 / 3

P = 12000

The sum is ₹12000.

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