Question

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. 7
• B. 9
• C. 8
• D. 6

Answer 1

The Correct Option is B

Let ₹x lakhs be the amount invested in the fixed deposit. Then, the remaining ₹(15 - x) lakhs is invested elsewhere, split into two-thirds and one-third at different rates. 

According to the problem:

\[ \text{Total Interest} = x \times \frac{6}{100} + \frac{2}{3}(15 - x) \times \frac{4}{100} + \frac{1}{3}(15 - x) \times \frac{3}{100} \]

Given total interest earned = ₹76,000 = \(\frac{76000}{100000} = 0.76\) lakhs

Step-by-Step Simplification:

\[ \Rightarrow 0.06x + \frac{2}{3}(15 - x) \cdot 0.04 + \frac{1}{3}(15 - x) \cdot 0.03 = 0.76 \]

First calculate the second and third terms:

\[ \frac{2}{3}(15 - x) \cdot 0.04 = \frac{2 \cdot 0.04}{3}(15 - x) = \frac{0.08}{3}(15 - x) \] \[ \frac{1}{3}(15 - x) \cdot 0.03 = \frac{0.03}{3}(15 - x) = \frac{0.03}{3}(15 - x) \]

Add both parts: \[ \frac{0.08 + 0.03}{3}(15 - x) = \frac{0.11}{3}(15 - x) \]

So full equation becomes: \[ 0.06x + \frac{0.11}{3}(15 - x) = 0.76 \]

Multiply through by 3 to eliminate denominator: \[ 0.18x + 0.11(15 - x) = 2.28 \] \[ 0.18x + 1.65 - 0.11x = 2.28 \] \[ 0.07x = 2.28 - 1.65 = 0.63 \] \[ x = \frac{0.63}{0.07} = 9 \]

Answer:

₹9 lakhs was invested in the fixed deposit.