Question

If twice the son’s age in years is added to the father’s age, the sum is 70. But if twice the father’s age is added to the son’s age, the sum is 95. Find the ages of father and son?

Answer 1

Hint: We start solving the problem by assigning the variables for the ages of father and son. We then find our first relation between these variables by using the given statement that the sum of twice the age of son and age of the father is 70 years. We then find our second relation between these variables by using the given statement that the sum of twice the age of father and age of the son is 95 years. We then make the necessary calculations between the two obtained relations to find the ages of father and son.

Complete step-by-step solution:
According to the problem, we are given that if twice the son’s age in years is added to the father’s age, the sum is 70 and if twice the father’s age is added to the son’s age, the sum is 95. We need to find the ages of father and son.
Let us assume the ages of father and son be ‘x’ and ‘y’.
We are given that the sum of twice the age of son and age of the father is 70 years.
So, we get $x+2y=70$ ---(1).
We are also given that the sum of twice the age of father and the age of the son is 95 years.
So, we get $2x+y=95$.
$\Rightarrow y=95-2x$ ---(2).
Let us substitute equation (2) in equation (1).
So, we get $x+2\left( 95-2x \right)=70$.
$\Rightarrow x+190-4x=70$.
$\Rightarrow -3x=-120$.
$\Rightarrow x=40$. Let us substitute this in equation (2).
So, we get $y=95-2\left( 40 \right)$.
$\Rightarrow y=95-80$.
$\Rightarrow y=15$.
So, we have found the ages of father and son as 40 years and 15 years.

Note: Whenever we get this problem, we first assign variables to the unknowns to avoid confusion while making calculations. We can also find the ages by using trial and error methods for father and son. We can also find the difference between the age of father and son using the obtained values. Similarly, we can expect problems to find the sum of the ages obtained.