The simple interest on a certain sum of ₹ P at a rate of r% per annum for 3 years is Rs.11,250 and the compound interest on the same sum for 2 years at the same rate percent p.a. is ₹ 7,650. What is the value of P and r, respectively?

Question

Question

This question was previously asked in

SSC Graduation Level Previous Paper (Held on: 14 March 2022 Shift 3)

Attempt Online

Answer 1

Given data:

SI for 3 years = Rs 11,250

CI for 2 years at the same rate = Rs 7650

Formula used:

P = \(SI\times 100\over {R\times T}\) where-

P = Principal

SI = Simple Interest

R = Rate

T = Time

Calculation:

SI for 1 year = 11,250 ÷ 3 = Rs 3,750

SI for 2 year = 2 × 3750 = Rs 7500

Difference between CI and SI for 2 year = 7650 - 7500 = Rs 150

⇒ This difference between CI and SI was on the SI for the 1st year i.e., Rs 3750

∴ Rate % = \(150\over 3750\) × 100 = 4%

Principal = \(3750\times 100\over {1\times4}\) = Rs 93,750

∴ The Principal amount was Rs 93,750 and the rate of interest was 4%.