Question

Two years ago, father was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Find their present age.

Answer 1

Hint: Here we will assume the unknown age of Son to be “x” and then frame the mathematical expression, finding the correlation between the father’s and Son’s age and will simplify for the value of “x” and then for their present ages.

Complete step-by-step answer:
Let us assume that, the present age of Son be $ = x $ years
Son’s age before two years ago $ = x - 2 $ years
Given that: Two years ago, the father was three times as old as his son. Convert the given statement in the form of the mathematical expressions.
Father’s age before two years $ = 3(x - 2) $ years
Now, the age of father after two years $ = 3(x - 2) + 2 $
Simplify the above expression –
 $ = 3x - 6 + 2 $
When you combine two terms, one negative term with one positive term you have to subtract and give negative sign to the resultant value.
Father’s age after two years $ = 3x - 4 $
Son’s age after two years $ = x + 2 $
Also, given that - twice the father's age will be equal to five times that of his son. Convert the above statement in the form of mathematical expression.
 $ 5(x + 2) = 2(3x - 2) $
Open the brackets multiplying the terms inside the bracket –
 $ \Rightarrow 5x + 10 = 6x - 4 $
Move the constants on the left hand side of the equation and the term with the variable on the right hand side of the equation. When you move any term from one side to the other then the sign of the term also changes. Positive term becomes negative and vice-versa.
 $ \Rightarrow 10 + 4 = 6x - 5x $
Simplify the above expression –
 $ \Rightarrow x = 14 $ years
Now, father’s age $ = 3x - 4 $
Place the value of “x” in the above expression –
father’s age $ = 3(14) - 4 = 42 - 4 = 38 $ years
Hence, the son’s age is $ 14 $ years and father’s age is $ 38 $ years.

Note: Be careful about the sign convention while simplifying the equations. Always remember the value received in terms of ages can never be negative. Cross- check the values received with the given data whether it is twice or thrice as per the data.