Question

Sachin is younger than Rahul by 4 yrs. If their ages are in the respective ratio of $7:9$, how old is Sachin ?
A. $16$ years
B. $18$ years
C. $14$ years
D. $15$ years

Answer 1

Hint- In order to solve this kind of problem first we have to take the present age of the people in variable and later on according to the question we can write the equation. In this question We know the ages ratio of Sachin and rahul.

Complete step by step solution:
Given that Sachin is younger than Rahul by $4$ years and their ages are in respective $7:9$ ratio.
Let us assume Rahul age is $x$ years.
$\because $ Sachin is younger than Rahul by $4$ years.
So, Sachin age be $ = (x - 4)$ years.
According to the question the ages ratio will be
$ \Rightarrow \dfrac{{{\text{Sachin's age}}}}{{{\text{Rahul's age}}}} = \dfrac{7}{9} \to (1)$
By putting the values in equation 1 we get
$ \Rightarrow \dfrac{{(x - 4)}}{x} = \dfrac{7}{9}$
By cross multiplication we get
$9(x - 4) = 7x$
Further solving this equation we get
$
   \Rightarrow 9(x - 4) = 7x \\
   \Rightarrow 9x - 36 = 7x \\
   \Rightarrow 9x - 7x = 36 \\
   \Rightarrow 2x = 36 \\
   \Rightarrow x = \dfrac{{36}}{2} \\
   \Rightarrow x = 18 \\
$
$\therefore x = 18{\text{ years}}$
We assumed that Rahul’s age is $x$ years
And Sachin’s age is $(x - 4){\text{ years}}$
So Sachin’s age is $(18 - 4) = 14{\text{ years}}$
Hence, Sachin's age is $14{\text{ years}}$ and C is the correct option.

Note- Ages related questions are based on simple calculation with linear equations. Questions may be provided the age ratio or different relationship with respect to time. We can assume the present age in variable and solve the question further. When time increases, age will also increase and if time decreases then age will also decrease.