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CAT 2019 Slot 1 — QA Question 29

Simple InterestEasy

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 76,000 then the amount (in Rs lakh) invested in the fixed deposit was

Answer & solution

Answer: 9

Solution

Easy

Let the two ratio-deposits be 2x2x and xx (lakh), so the fixed deposit is 15−3x15-3x. Write the simple interest from each at its rate, set the total to Rs 76,000, solve for xx, then report the fixed-deposit amount.

Total =15=15 lakh. Fixed deposit at 6%6\%. Remaining split 2:12:1 at 4%4\% and 3%3\%. Total interest == Rs 76,000=0.7676{,}000=0.76 lakh.

1

Name the parts (in lakh). Let the 2:12:1 deposits be 2x2x and xx.

Fixed deposit=15−(2x+x)=15−3x\begin{aligned} &\text{Fixed deposit}=15-(2x+x)=15-3x \end{aligned}
2

Interest equation. Sum the three simple-interest amounts (in lakh) at 6%,4%,3%6\%,4\%,3\%.

0.06(15−3x)+0.04(2x)+0.03(x)=0.76(76,000=0.76 lakh)⇒ 0.9−0.18x+0.08x+0.03x=0.76⇒ 0.9−0.07x=0.76\begin{aligned} &0.06(15-3x)+0.04(2x)+0.03(x)=0.76\quad\text{(}76{,}000=0.76\text{ lakh)}\\ &\Rightarrow\ 0.9-0.18x+0.08x+0.03x=0.76\\ &\Rightarrow\ 0.9-0.07x=0.76 \end{aligned}
3

Solve and report. Isolate xx, then compute the fixed deposit.

0.07x=0.14 ⇒ x=2(from step 2)⇒ Fixed deposit=15−3(2)=9 lakh\begin{aligned} &0.07x=0.14\ \Rightarrow\ x=2\quad\text{(from step 2)}\\ &\Rightarrow\ \text{Fixed deposit}=15-3(2)=9\ \text{lakh} \end{aligned}
Fixed deposit=9 lakh\text{Fixed deposit}=9\ \text{lakh}
CAT 2019 Slot 1 QA Q29: A person invested a total amount of Rs 15 lakh. A part of it was invested in a fixed deposit earning 6% annual — Solution | TheCATExam