Multiple choice

Which information is/are sufficient to answer the questions asked? A sum of money is put at CI. Find the rate percent when the interest is reckoned yearly. I. The ratio of SI to CI at the end of 3 years on the same sum and same rate of interest is 300: 331. II. If the same sum is put at SI for 5 years on the same rate of interest then the SI will be 50% less than the principal amount. III. The difference between CI and SI at the end of 2 years on the same sum and same rate of interest is Rs 200.

  1. Any two of them

  2. III and (I or II)

  3. I or II alone is sufficient

  4. II or (I and III)

  5. None of these
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C Correct answer
Explanation

Statement II directly gives the rate: SI for 5 years is 50% of principal, so 5r/100 = 50/100, giving r = 10%. Statement I gives the ratio SI/CI = 300/331 after 3 years. For principal P and rate r, SI = 3Pr/100, CI = P(1 + r/100)^3 - P. Setting their ratio equal to 300/331 gives an equation solvable for r. Statement III alone gives CI - SI = Pr^2/10000 for 2 years, but requires P, so not sufficient alone. Therefore, I or II alone is sufficient.

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