Rs.26000 is split into two sums such that the Simple Interest on one part for 5 years at 10% equals the Simple Interest on the other part for 6 years at 9%. What is the sum placed at 10% for 5 years?
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A.
Rs.15000
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B.
Rs.12500
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C.
Rs.14000
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D.
Rs.13500
Correct Answer:
D. Rs.13500
Explanation:
To find the sum placed at 10%, let the two parts of the Rs. 26,000 be x and (26,000 - x). According to the simple interest formula (Principal × Rate × Time / 100), the interest for the first part is (x × 10 × 5) / 100, and for the second part, it is ((26,000 - x) × 9 × 6) / 100. Setting these interests equal gives 50x = 54(26,000 - x). Simplifying this equation leads to 50x = 1,404,000 - 54x, which further simplifies to 104x = 1,404,000. Dividing 1,404,000 by 104 results in x = 13,500. Thus, the amount invested at 10% for 5 years is Rs. 13,500.
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