Amita is a 2 years older than her friend Amrita. Amita's father is twice as old as Amita, and Amrita is twice as old as her sister. The ages of Amita's father and Amrita's sister differ by 43 years. The sum of the ages (in years) of Amita and Amrita is:

Correct option is A

Given:

Amita is 2 years older than Amrita

Amita's father = 2 × Amita’s age

Amrita = 2×Amrita’s sister’s age

Difference between Amita's father and Amrita's sister = 43 years

Solution:

Let Amrita’s sister’s age be x.

$$\text{Amrita's age} = 2x, \\ \ \\\text{Amita's age} = 2x + 2, \\ \ \\ \text{Amita's father's age} = 2(2x + 2)$$ 

Now, 

​$$2(2x + 2) - x = 43$$

​$$4x + 4 - x = 43 \\ \ \\ \Rightarrow \quad 3x = 39 \\ \ \\ \Rightarrow \quad x = 13$$ 

So, 

​$$\text{Amrita's age} = 2x = 26, \\ \ \\ \text{Amita's age} = 26 + 2 = 28$$​

Sum of their ages = 26 + 28 = 54 years