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Amala, Bina, and Gouri invest money in the ratio $3:4:5$ in fixed deposits having respective annual interest rates in the ratio $6:5:4$. what is their total interest income (in Rs) after a year, if Bina’s interest income exceeds Amala’s by Rs $250$?

  1. $6350$
  2. $7250$
  3. $7000$
  4. $6000$
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Let money invested by Amala, Bina, and Gouri be $ 3x, 4x,$ and $5x$. And the annual interest rates be $ 6y,5y,$ and $4y$ respectively.

We know that,

  • Interest income $\propto$ Amount invested
  • Interest income $\propto$ Interest rate

Therefore, interest income must be in the ratio of the product of their amount invested and interest rate.

  • Amala’s interest income $ = 3x \times 6y = 18xy $
  • Bina’s interest income $ = 4x \times 5y = 20xy $
  • Gouri’s interest income $ = 5x \times 4y = 20xy $

Bina’s interest income exceeds Amala’s by $\text{Rs}. 250 $

$ 20xy – 18xy = 250 $

$ \Rightarrow 2xy = 250 $

$ \Rightarrow xy = 125 $

$\therefore$ Total interest income after a year $ = 18xy + 20xy + 20xy $

$ \quad = 58xy  = 58 \times 125 = \text{Rs}. 7250.$

$\textbf{Short Method:}$

$\begin{array}{lccc} & \text{Amala} & \text{Bina} & \text{Gouri} \\ \text{Invest} & 3 & 4 & 5 \\ \text{Interest rate} & 6 & 5 & 4 \\ \text{Interest income} & {\color{Red} {18}} & {\color{Blue} {20}} & 20 \end{array}$

According to the question,

  • $2 \longrightarrow 250$
  • $1 \longrightarrow  125$

Therefore, total interest income (in Rs) after a year $ = (18 + 20 + 20) \times 125 = 58 \times 125 =  \text{Rs}. 7250.$

Correct Answer $: \text{B}$

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