Question

Rohit father is 27 years older than him and after 5 years their age ratio is 2:3 find their age​

Answer 1

$\bf{\large{\underline{\underline{Answer:-}}}}$

The ages of Rohit and Rohit's father are 49 years and 76 years respectively.

$\bf{\large{\underline{\underline{Explanation:-}}}}$

Given :- Rohit father is 27 years older than him. After 5 years their age ratio is 2 : 3

To find :- Their ages

Solution :-

Let the age of Rohit be x

Rohit's father age = 27 years older than Rohit = (x + 27)

After 5 years :-

Rohit's age = (x + 5)

Rohit's father age = [(x + 27) + 5] = (x + 27 + 5) = (x + 32)

Ratio of ages of Rohit and Rohit's father after 5 years = 2 : 3

According to the question :-

Equation formed :-

$\boxed{\tt{ \dfrac{x + 5}{x + 32} = \dfrac{2}{3} }}$

By Cross multiplication

$\tt{\implies{(x + 5)3 = 2(x + 32)}}$

$\tt{\implies{3x + 15 = 2x + 64}}$

$\tt{\implies{3x - 2x = 64 - 15}}$

$\tt{\implies{x = 49}}$

Rohit's age = x = 49 years

Rohit's Father age = (x + 32) = (49 + 27) = 76 years

$\bf{\large{\underline{\underline{Verification:-}}}}$

To know whether the answer is correct or not substitute ages of Rohit and Rohit's father age in the equation that is formed to solve.

$\tt{ \dfrac{49 + 5}{76 + 5} = \dfrac{2}{3} }$

$\tt{\implies{ \dfrac{54}{81} = \dfrac{2}{3} }}$

$\tt{\implies{\dfrac{54 \div 27}{81 \div 27} = \dfrac{2}{3} }}$

$\tt{\implies{ \dfrac{2}{3} = \dfrac{2}{3} }}$

Therefore the ages of Rohit and Rohit's father are 49 years and 76 years respectively.