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Find the value of x. Statement I: A person lent out a sum of Rs. 2400 in the ratio of 5 : x in Scheme A and Scheme B, respectively. Scheme A is offering simple interest at 8% per annum and Scheme B is offering simple interest at 3(x+1)% per annum. The interest earned from Scheme A after 2 years is Rs. 24 more than the interest earned from Scheme B after 2 years. Statement II: A person lent out a sum of Rs. 2400 in the ratio of 5 : 3 in Scheme A and Scheme B, respectively. Scheme A is offering simple interest at 8% per annum and Scheme B is offering simple interest at 3(x+1)% per annum. The simple interest earned from Scheme A after 9 years is equal to the interest earned from Scheme B after (x+7) years.
- If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
- If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
- If the data either in statement I alone or in statement II alone is sufficient to answer the question
- If the data in both statements I and II together are necessary to answer the question
Correct answer: If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
Solution
Statement I gives the investment split as 5:x and also provides a direct interest difference after the same time period, which is enough to form one equation in x. Statement II does not uniquely determine x because the ratio is fixed at 5:3 while x appears only in the rate and time relation, making it insufficient on its own.
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