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Arun invested a certain sum of money at a rate of interest of 9% per annum. If the ratio of the amount to interest is 216:91, then which of the following rate-time combinations is correct? I: 10%, 2 years II: 20%, 3 years III: 25%, 3 years

1. Only I
2. Only II
3. Both I and II
4. Both II and III

Correct answer: Only II

Solution

If A:I = 216:91, then let A = 216k and I = 91k, so principal P = A − I = 125k. Under simple interest, I = PRT/100, hence 91k = 125k × R × T / 100, giving RT = 72.8, which matches 20% for 3 years only among the options.

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