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 ★

• $\bf{Cousin's \ age \ = \ 52 years}$

• $\bf{Raju's \ age \ = \ 33 years}$

Given :

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

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

To find :

• Their present ages ?

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 :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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

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

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

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

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

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

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

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

Raju's age :⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf x - 19$

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

$:\implies\sf 52 - 19$

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

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

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

Answer 2

Answer:

Given :-

Raju age is 19 years younger than his cousin.After five years their age will be in the ratio of 2:3.

To Find :-

what is their present ages?

Solution :-

Let, the present age of Raju be x

And, the present age of Raju's cousin be y

After 5 years,

Raju's age is x + 5

And, his cousin is 19 + x + 5 = 24 + x

Ratio of their age = 2:3

According to the question,

⇒ $\dfrac{x + 5}{24 + x}$ = $\dfrac{2}{3}$

⇒ 3(x + 5) = 2(24 + x)

⇒ 3x + 15 = 48 + 2x

⇒ 3x - 2x = 48 - 15

⇒ x = 33

Hence, the required ages,

Present age of Raju's is = x = 33 years

And, present age of his cousin = 19 + x = 19 + 33 = 52 years