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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. $6000$

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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