Multiple choice

Sushmita invests a certain sum of money for 3 years at 10% pa at simple interest rate. The SI accrued is half the CI on Rs. 10000 for 2 years at 10% pa. Find the sum placed on simple interest?

  1. ₹ 3200

  2. ₹ 3500

  3. ₹ 3000

  4. ₹ 1050

  5. ₹ 1000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

CI on 10000 for 2 years at 10% = 10000 * (1.1^2 - 1) = 2100. SI = 2100 / 2 = 1050. SI = P * R * T / 100 -> 1050 = P * 10 * 3 / 100 -> 1050 = 0.3P -> P = 3500.

AI explanation

First, calculate the compound interest on Rs. 10000 for 2 years at 10% using the formula CI = P[(1 + R/100)^T - 1], which gives 10000[(1.1)^2 - 1] = 10000(1.21 - 1) = Rs. 2100. The simple interest accrued is half of this, so SI = Rs. 1050. Using the simple interest formula SI = P * R * T / 100, we have 1050 = P * 10 * 3 / 100, which simplifies to 1050 = 0.3P, meaning the sum invested is Rs. 3500.

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