Question

raju is 19 years younger than his cousin . after five years, their ages will be in the ratio 2:3 . find their present ages.​

Answer 1

Answer:

ANSWER

Let cousin's age be x

So, Raju's age will bex−19

After 5 years ratio of their ages will be=

3

2

So,

x+5

x−19+5

=

3

2

x+5

x−14

=

3

2

3x−42=2x+10

3x−2x=42+10

x=52

x−19=52−19=33

Therefor present age of Raju is 33 years and present age of his cousin is 52years.

Answer 2

$\underline{ \mathfrak{ \: Given:- \: }}$

• Raju's age is 19 years younger than his cousin.

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

$\underline{ \mathfrak{ \: To \ Find:- \: }}$

• Present ages ?

$\underline{ \mathfrak{ \: Solution:- \: }}$

☯ Let the present age of Raju and his cousin be x years.

⠀⠀⠀

• Then Raju's present age will be 5 years (x - 19) years.

⠀⠀⠀⠀⠀⠀⠀⠀

• Raju's cousin's age will be (x + 5) years.

⠀⠀⠀⠀⠀⠀⠀⠀

• Raju's age will be (x - 19 + 5) = (x + 14) years. ⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

Cousin's age :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf{\dfrac{x - 14}{x + 5}}$ = $\sf{\dfrac{2}{3}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 3 ( x - 14 ) = 2 ( x + 5 )$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 3x - 42 = 2x + 10$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 3x - 2x = 10 + 42$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies{\boxed{\frak{\purple{x = 52}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{∴ \ Thus , \ Cousin's \ age \ is \ 52 \ years.}$

Raju's age :⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf x - 19$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf 52 - 19$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies{\boxed{\frak{\purple{33 \: years}}}}\;\bigstar$

$\sf{∴ \ Thus \ , Raju's \ age \ is \ 33 \ years}$