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      Question

      The question consists of two

      statements numbered "I and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Find the rate of interest per annum? Statement I: A sum of money becomes 5 times of itself in 20 years on simple interest. Statement II: An amount invested on simple interest becomes Rs. 4,500 in 6 years.
      A The data in statement I alone are sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B The data in statement II alone are sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C The data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
      D The data given in both statements I and II together is not sufficient to answer the question. Correct Answer Incorrect Answer
      E The data in both statements I and II together is necessary to answer the question. Correct Answer Incorrect Answer

      Solution

      ATQ,

      Statement I: Let the principal be Rs. ‘P’ and the rate of interest be ‘R’% per annum. Simple Interest earned in 20 years = (P × R × 20) ÷ 100 = 0.20PR Total Amount after 20 years = 5P So, 5P – P = 0.20PR Or, 4P = 0.20PR Or, R = (4 ÷ 0.20) = 20% So, the rate of interest is 20% per annum. Hence, data in Statement I alone is sufficient. Statement II: Simple Interest for 6 years = (P × R × 6) ÷ 100 = 0.06PR Total Amount = P + 0.06PR = 4,500 So, P(1 + 0.06R) = 4,500 Here, we have two unknowns (P and R). Without more info, R cannot be determined. Hence, data in Statement II alone is not sufficient. Hence, Data in Statement I alone is sufficient, while Statement II alone is not sufficient.

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