Multiple choice

The simple interest on a certain sum of money for $3$ years at $8\%$ per annum is half the compound interest on $Rs.\,4000$ for $2$ years at $10\%$ per annum. The sum placed on simple interest is .............. .

  1. $Rs.\,1550$
  2. $Rs.\,1650$
  3. $Rs.\,1750$
  4. $Rs.\,2000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Compound interest on 4000 for 2 years at 10% is 4000 * (1.1^2 - 1) = 840. Simple interest is half of this, 420. Using SI = (P * R * T) / 100: 420 = (P * 8 * 3) / 100 => 42000 = 24P => P = 1750.

AI explanation

Using the compound interest formula, the CI on Rs. 4000 for 2 years at 10% is 4000 * (1 + 10/100)^2 - 4000 = 4840 - 4000 = Rs. 840. The given simple interest is half of this, which is Rs. 420. Setting up the simple interest equation 420 = (P * 8 * 3) / 100 gives 24P = 42000, so the sum placed on simple interest is Rs. 1750.

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