Multiple choice

The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23 : 7 respectively. What is rate of interest per annum (in %)?

  1. 200/7

  2. 200/9

  3. 300/7

  4. 100/7
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A Correct answer
Explanation

For 2 years: CI - SI = P[(1 + r/100)² - 1 - 2r/100] = Pr²/10000. For 3 years: CI - SI = P[(1 + r/100)³ - 1 - 3r/100] = P[3r²/10000 + r³/10^6]. Ratio = [3r²/10000 + r³/10^6] : [r²/10000] = 23 : 7. This gives (3 + r/100) : 1 = 23 : 7, so 3 + r/100 = 23/7, giving r/100 = 2/7, hence r = 200/7%.

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