Multiple choice

A sum of money is put at compound interest for 2 years. What is the rate of interest per annum? Statement I: If the same amount of money is put at simple interest for three years then the amount of interest is Rs.600 more than the interest amount calculated on CI at the end of 2 years. Statement II: The simple interest on the same sum at the end of four years is Rs.3200 Statement III: Sum of money becomes 4 times in two years at compound interest

  1. Either statement III alone or statements I and II together are sufficient.

  2. Only statement III is sufficient.

  3. Statement I and Statement III together are sufficient.

  4. Only statement I, II, and III together are sufficient.

  5. None of these
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A Correct answer
Explanation

Statement III: Sum becomes 4 times in 2 years at CI, so (1+r/100)²=4, which gives 1+r/100=2, so r=100%. This alone is sufficient. Alternatively, using Statement I and II together: Let P be principal. From II, SI for 4 years = 3200, so 4PR/100 = 3200, PR=80000. From I, SI(3y) - CI(2y) = 600. 3PR/100 - P[(1+r/100)²-1] = 600. Substituting PR=80000 gives r=100%. Either III alone OR I and II together work.

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