Let the age of A be a years.
According to the question:
- A is elder to B by 2 years, so B’s age is b = a – 2.
- Father F is twice as old as A, thus f = 2a.
- B is twice as old as his sister S, leading to s = b / 2 or s = (a – 2) / 2.
We also know the age difference between Father F and Sister S is 40 years:
f – s = 40
Substituting the values of F and S into the equation:
2a – (a – 2) / 2 = 40
Now, multiply through by 2 to eliminate the fraction:
4a – (a – 2) = 80
Distributing gives:
4a – a + 2 = 80
This simplifies to:
3a + 2 = 80
Subtracting 2 from both sides yields:
3a = 78
Dividing both sides by 3 gives:
a = 26
Thus, the age of A is 26 years.