Investment Split into Fixed and Multiple Deposits

CAT 2019 Slot 1 · QA · Easy · Simple interest

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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%6\% annual interest, and the remaining amount was invested in two other deposits in the ratio 2:12 : 1, earning annual interest at the rates of 4%4\% and 3%3\%, respectively. If the total annual interest income is Rs 76000 then the amount (in Rs lakh) invested in the fixed deposit was

Answer

9

Explanation

Let fixed deposit be xx lakh. Remaining deposit =(15−x)= (15 - x) lakh. Remaining is split as 23(15−x)\frac{2}{3}(15-x) at 4%4\% and 13(15−x)\frac{1}{3}(15-x) at 3%3\%. Effective interest rate on remaining =2(4%)+1(3%)3=113%= \frac{2(4\%) + 1(3\%)}{3} = \frac{11}{3}\%. Total interest: 0.06x+0.113(15−x)=0.760.06x + \frac{0.11}{3}(15-x) = 0.76. 0.18x+1.65−0.11x=2.28  ⟹  0.07x=0.63  ⟹  x=90.18x + 1.65 - 0.11x = 2.28 \implies 0.07x = 0.63 \implies x = 9 lakh.

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