CAT 2019 Quant Question with Solution 30

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

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Correct Answer: 9

Let the amount invested in fixed deposit be x lakhs.

As per the condition:

$x\times \frac{6}{100}+\frac{2}{3}\times \left( 15-x \right)\times \frac{4}{100}+\frac{1}{3}\times \left( 15-x \right)\times \frac{3}{100}=\frac{76000}{{{10}^{5}}}$

$\Rightarrow 6x-\frac{8}{3}x-x=76-\frac{8}{3}\times 15-15$

$\Rightarrow \frac{7}{3}x=\frac{76\times 3-11\times 15}{3}$

$\Rightarrow \frac{7}{3}x=\frac{63}{3}$

$\Rightarrow x=9$

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