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 suicient to answer the question. Arjun invested different sums of money in two separate banks: SBI and PNB. The rate of simple interest provided by SBI is 7% per annum, whereas PNB offers 14% per annum. Determine the amount Arjun deposited in the SBI bank. Statement I: The total simple interest earned from both banks together in 2 years is 1106. Statement II: The total simple interest earned from both banks together in 3 years is 1659.Solution
ATQ,
Suppose the amounts invested in SBI Bank and PNB Bank are Rs. ‘x’ and Rs. ‘y’, respectively. Statement I: The simple interest from SBI at 7% for 2 years and from PNB at 14% for 2 years totals Rs. 1106: (x × 7 × 2)/100 + (y × 14 × 2)/100 = 1106 ⇒ 0.14x + 0.28y = 1106 ---------(1) Thus, Statement I alone does not provide enough data to solve for ‘x’ and ‘y’. Statement II: The simple interest from SBI at 7% for 3 years and from PNB at 14% for 3 years totals Rs. 1659: (x × 7 × 3)/100 + (y × 14 × 3)/100 = 1659 ⇒ 0.21x + 0.42y = 1659 ----------(2) So, Statement II alone is also insufficient to find the values of ‘x’ and ‘y’. Combining both statements: 0.14x + 0.28y = 1106 ---------(1) 0.21x + 0.42y = 1659 ----------(2) Since equation (2) is just 1.5 times equation (1), both equations represent the same linear relationship. As a result, ‘x’ and ‘y’ cannot be uniquely determined. Therefore, even both statements together are insufficient to answer the question.
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