Question

18. Raju is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2:3.
Find their present ages.
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Answer 1

Given :

• Raju is 19 years younger than his cousin.
• After 5 years, their ages will be in the ratio 2:3.

To Find :

• Present Age of Raju and his cousin .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:cousin\:be=x}$

As Given that Raju is 19 years younger than his cousin. So ,

$\longmapsto\tt{Age\:of\:Raju=x-19}$

After 5 years :

$\longmapsto\tt{Age\:of\:Raju=x-19+5=x-14}$

$\longmapsto\tt{Age\:of\:Cousin=x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-14}{x+5}=\dfrac{2}{3}}$

$\longmapsto\tt{3(x-14)=2(x+5)}$

$\longmapsto\tt{3x-42=2x+10}$

$\longmapsto\tt{3x-2x=10+42}$

$\longmapsto\tt\bf{x=52}$

Value of x is 52 .

Therefore :

$\longmapsto\tt{Age\:of\:Cousin=x}$

$\longmapsto\tt\bf{52\:yrs}$

$\longmapsto\tt{Age\:of\:Raju=52-19}$

$\longmapsto\tt\bf{33\:yrs}$

Answer 2

Given :

• Raju is 19 years younger than his cousin. After 5 years, their ages will be in the ratio 2:3 .

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To Find :

• Find the present age.

$\rule{200pt}{3pt}$

Solution :

$\pink{❒}$According to Question :

✏ Let age of Cousins be y.

Raju is 19 years younger than his cousin .

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{Age \: of \: Raju}{Age \: of \: Cousion} = \dfrac{y - 19}{y}}}}}}}{\bigstar}}$

After 5 years, their ages will be in the ratio 2:3 .

$\qquad{\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{y - 19 + 5}{y + 5} = \dfrac{2}{3}}}}}}}{\bigstar}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\pink{❒}$Let's Cross Multiply :

${\longmapsto{\qquad{\rm{ 3(y - 19 + 5) = 2(y + 5) }}}} \\ \\ \ {\longmapsto{\qquad{\rm{ 3(y - 14) = 2(y + 5)}}}} \\ \\ \ {\longmapsto{\qquad{\rm{ 3y - 42 = 2y + 10 }}}} \\ \\ \ {\longmapsto{\qquad{\rm{ 3y - 2y = 42 + 10 }}}} \\ \\ \ {\qquad{\rm{Value \: of \: y \: = {\green{\rm{52 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\pink{❒}$Calculating the Ages :

Age of Raju :

$\large{\orange{\longmapsto{\underline{\underline{\color{red}{\sf{ Raju = y - 19 = 52 - 19 = 33 \: years }}}}}}}$

$\large{\orange{\longmapsto{\underline{\underline{\color{red}{\sf{ Cousin = y = 52 \: years }}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━}$

$\pink{❒}$Therefore :

❝ Age of Raju is 33 years and the age of his cousin is 52 years. ❞

$\rule{200pt}{7pt}$