Step 1: Define variables for each person's age

Let Amrita's age be $x$. Since Amita is 2 years elder than Amrita, Amita's age is $x + 2$. Amrita is twice as old as her sister, so her sister's age is $\frac{x}{2}$. Amita's father is twice as old as Amita, so the father's age is $2(x + 2)$.

$\text{Amrita} = x, \quad \text{Amita} = x + 2, \quad \text{Sister} = \frac{x}{2}, \quad \text{Father} = 2(x + 2)$

Step 2: Formulate the equation using the given age difference

We are given that the ages of Amita's father and Amrita's sister differ by 43 years. Setting up this equation gives: $2(x + 2) - \frac{x}{2} = 43$

$2(x + 2) - \frac{x}{2} = 43$

Step 3: Solve the equation for $x$

Expanding and simplifying the equation: $2x + 4 - 0.5x = 43 \implies 1.5x = 39 \implies x = 26$ Thus, Amrita's age is $26$ years.

$x = 26$

Step 4: Find the difference between Amita's and Amrita's ages

Amrita's age is $x = 26$ years. Amita's age is $x + 2 = 28$ years. The difference between Amita and Amrita is $28 - 26 = 2$ years.

$\text{Difference} = 28 - 26 = 2 \text{ years}$