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 $: \text{B}$