Question

When the son will be as old as his father today, the sum of their ages then will be 126. When the father was as old as his son is today, the sum of their ages was 38. Find their present ages.

Answer 1

Hint: In these types of questions use the given information to form the equation such as make one equation while considering the previous age of father and son then make a second equation using the new age of father and son use this information to get a better approach in this question.

Complete step-by-step solution:

In this question we have asked their present age, So, let us take the son’s current age” x “and father’s current age” y”. The question says that the son is going to be as old as the father is today, meaning the son has to live a certain number of years. How many years will he be aging? The difference between his current age and the current age of his father. So, to calculate a son’s age the son has to live certain years to reach his current age which means that if the son is 20 years old and the father was 50 years old, it would take the son 30 years to reach his current age which means the equation which will form will be : (y-x).

According to the question,

So, $\text{[father’s new age]} + \text{[son’s new age]}$ = 126

Therefore the equation will be $[y + (y - x)] + [(x + (y - x))] =126$

$ \Rightarrow 2y - x + y=126$

$ \Rightarrow 3y - x =126 $ ……………….(equation 1)

Similarly, $\text{[father’s previous age]} + \text{[son’s previous age]}$ =38

Thus the equation is $[y - (y - x)] + [x - (y - x)] =38$

$ \Rightarrow – x – y =38$

$ \Rightarrow 3x-y=38 $

$ \Rightarrow y = 3x – 38 $ …………………..(equation 2)

Now substituting the value of y in equation (1)

$ \Rightarrow 3(3x – 38) - x =126$

$ \Rightarrow 9x -114 - x=126$

$ \Rightarrow 8x = 240$

$ \Rightarrow x=30 $

Therefore the son’s present age is 30

Now for father’s age substituting the value of x in equation 2

$Y = 3(30) - 38 $

$ \Rightarrow y = 52 $

Hence, the son is 30 years old and the father is 52 years old.

Note: The equations we made using the given information in the above solution are linear equations, but what is a linear equation so the linear equation can be explained as equations that have only 2 variables the general form of a linear equation is $ax + by + c = 0$, for example, $2x + 3y + 6 = 0$.