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A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was
A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual interest, and the remaining amount was invested in two other deposits in the ratio 2 : 1, earning annual interest at the rates of 4% and 3%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was
Updated On: Sep 13, 2024
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The Correct Option is B
Solution and Explanation
Let x represent the amount invested in the fixed deposit.
According to the given stipulation:
= \(x\times \frac{6}{100} + \frac{2}{3} \times (15-x) × \frac{4}{100} + \frac{1}{3} × (15-x) × \frac{3}{100} = \frac{76000}{10^5}\)
⇒ \(6x - \frac{8}{3x} - x = 76 - \frac{8}{3x} \times 15 - 15\)
⇒ \(\frac{7}{3} x = 76 \times 3 - 11 \times \frac{15}{3}\)
⇒ \(\frac{7}{3} x = \frac{63}{3}\)
⇒ x = 9
Therefore , amount invested in the fixed deposit was 9 lakhs
According to the given stipulation:
= \(x\times \frac{6}{100} + \frac{2}{3} \times (15-x) × \frac{4}{100} + \frac{1}{3} × (15-x) × \frac{3}{100} = \frac{76000}{10^5}\)
⇒ \(6x - \frac{8}{3x} - x = 76 - \frac{8}{3x} \times 15 - 15\)
⇒ \(\frac{7}{3} x = 76 \times 3 - 11 \times \frac{15}{3}\)
⇒ \(\frac{7}{3} x = \frac{63}{3}\)
⇒ x = 9
Therefore , amount invested in the fixed deposit was 9 lakhs
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