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:

Present age of Raju=33yrs

Present age of Raju cousin=52yrs

Step-by-step explanation:

Let the age of Raju be x

Then, his cousin age be x+19

Now,

Age of Raju after 5 yrs=x +5

And, age of Raju cousin after 5yrs=x+19+5=x+ 24

given,the ratio of their ages after 5 year is 2:3

therefore,x+5/x+24=2/3

by cross multiplication,

3(x+5)=2(x+24)

3x+15=2x+48

x=33

Now,

Present age of Raju=x=33yrs

Present age of Rajus cousin=x+19=52yrs

Hope it will help

MARK IT AS BRAINLIEST ANSWER

Answer 2

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 :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

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

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

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

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

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

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

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

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

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

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

Raju's age :⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf x - 19$

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

$:\implies\sf 52 - 19$

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

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

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

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