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?

The correct option is (b) or 7250.

Let the investments of Amala, Bina, and Gouri be $3x$, $4x$, and $5x$ respectively.
Let the annual interest rates of their deposits be $6y$, $5y$, and $4y$ respectively.

The interest income is computed as the product of investment and rate. Therefore:
Amala's interest income, $I_A=3x\cdot 6y=18xy$
Bina's interest income, $I_B=4x\cdot 5y=20xy$
Gouri's interest income, $I_G=5x\cdot 4y=20xy$

We are given that Bina's interest income exceeds Amala's by Rs 250:
$I_B-I_A=250$
$20xy-18xy=250$
$2xy=250\Rightarrow xy=125$.

The total interest income is:
$I_{total}=I_A+I_B+I_G=18xy+20xy+20xy=58xy$.

Substituting the value of $xy=125$:
$I_{total}=58\times 125=7250$ Rs.