Multiple choice

A sum of money amounts to Rs. 1500 after 3 years and Rs. 2000 after 5 years at the same rate of SI. What is the rate of interest per annum?

  1. 33.33%

  2. 45%

  3. 60%

  4. 30%

  5. None of these
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A Correct answer
Explanation

Let principal be P. After 3 years at simple interest: Amount = P + SI = P + (P × R × 3)/100 = Rs 1500. After 5 years: Amount = P + (P × R × 5)/100 = Rs 2000. The difference between 5-year and 3-year amounts represents interest for 2 years: (P × R × 5)/100 - (P × R × 3)/100 = 2000 - 1500, giving (P × R × 2)/100 = 500, so (P × R)/100 = 250. From the 3-year equation: P + 3 × 250 = 1500, so P = 750. Using (P × R)/100 = 250: (750 × R)/100 = 250, giving R = 25000/750 = 33.33%.

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