Multiple choice

Mohan Lal, the money lender, lent equal amounts to Gabbar and Thakur, 2 daily wagers, in the village of Ramgarh. The money to Gabbar was lent on compound interest (compounded annually) and that to Thakur on simple interest, the rate of interest being the same. The difference between the interest for a period of 2 years is Rs. 20 and that for 3 years is Rs. 64. What was the amount lent to each?

  1. Rs. 200

  2. Rs. 400

  3. Rs. 500

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let P be the principal and r be the rate. CI - SI for 2 years = P(r/100)^2 = 20. CI - SI for 3 years = P(r/100)^2 * (3 + r/100) = 64. Substituting the first into the second: 20 * (3 + r/100) = 64 => 3 + r/100 = 3.2 => r/100 = 0.2. Then P(0.2)^2 = 20 => P(0.04) = 20 => P = 500.

AI explanation

For compound interest, the difference between the interest for the third year and the interest for the second year is the interest earned on the first two years' compound interest. This difference is 64 - 20 = 44 rupees, which equals 20 multiplied by the rate divided by 100. Solving for the rate gives r = (44 divided by 20) multiplied by 100 = 20 percent. The difference in interest for the first 2 years is calculated as Principal multiplied by (r divided by 100) squared, so 20 = Principal multiplied by (20 divided by 100) squared. Solving this gives Principal = 20 divided by 0.04, which equals 500 rupees.

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