 QUESTION

# A is elder to B by two years. A's father F is twice as old as A and B is twice as old as his sister S. If the ages of father and sister differ by forty years, find the age of A.

Hint:- In this question assume the age of A will be $x$ hence the age of B will be $x - 2$ and the age of father will be $2x$. Then according to the given conditions make the relations in ages to find the age of A. This problem is based on linear equations.
Complete step-by-step solution -
Given that
A is elder to B by two years
Let the age of A be $x$
Then age of B is $= x - 2$......Take this as equation first
Also given that A's father F is twice as old as A and B is twice as old as his sister
Therefore age of father is $2x$
and consider the age of sister be $y$
Then age of B is $= 2y$.....Take this as equation second
Comparing equation first and second we get:
$\Rightarrow 2y = x - 2 \\ \Rightarrow y = \dfrac{{x - 2}}{2} \\$
Now it's given that ages of father and sister differ by forty years so we can write it as:
$\Rightarrow 2x - y = 40$
put the value of $y$ from above we get:
$\Rightarrow 2x - \dfrac{{\left( {x - 2} \right)}}{2} = 40 \\ \Rightarrow \dfrac{{4x - x + 2}}{2} = 40 \\ \Rightarrow \dfrac{{3x + 2}}{2} = 40 \\ \Rightarrow 3x + 2 = 80 \\ \Rightarrow 3x = 78 \\ \therefore x = 26 \\$
Therefore the age of A is $26$ years.
Note:- This question is based on a linear equation in two variables, so as the conditions given in question we formed the equation first and second and compared both the equations. Also it's given that the ages of father and sister differ by forty years hence we put the value in the equation $2x - y = 40$ and after simplifying it we got the value of $x$ which represents the age of A.