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# A father is now three times as old as his son. Five years ago he was four times as old as his son. The age of the son(in years) is A) $12$B) $15$C) $18$D) $20$

Last updated date: 13th Jun 2024
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Hint: Firstly we need to know about the age and then convert the problem in the form of the linear equation or we can say in terms of variables the in this type of the problem we need use the concept of the age After that we can calculate the value of the variables .

Complete step-by-step solution:
Let the age of the son is $x$ then age of the father is three times the age of the son then father age is $3x$
Five years back,
Age of the son $= x - 5$
Five years back age of the father$= 3x - 5$
According to the question
Fathers age $=$four times the age of the son
$\Rightarrow$$3x - 5 = 4\left( {x - 5} \right)$
Multiplied by $4$ in $x - 5$we get
$\Rightarrow$$3x - 5 = 4x - 20$
Rewrite the equation after simplification we get
$\Rightarrow$$4x - 3x - 20 + 5 = 0$
Rewrite the equation after simplification we get
$\Rightarrow$$x - 15 = 0$
$\Rightarrow$$x = 15$
Hence the age of the son is $15$

Option B is the correct answer.

Note: This type of problem is solved only by the concept of the age.
In other words we can say that the length of time during which a being or things has existed.
Length of life or existence to the time spoken of or referred to a period of human life , measured by years from birth.
Linear equations in one variable are used when we have one unknown quantity. If we have two unknown quantities we use linear equations in two variables.