Question

Raju is 19 years younger than his cousin. after 5 years the ratio of their ages will be 5:3 . find their present ages

Answer 1

Lets take Raju's cousin's age be x yrs
Therefore Raju 's age = x - 19
Ratio between Raju and his cousin = 2 : 3 or 2/3
Hence (x - 19) + 5/x + 5 = 2/3
= 5 + x - 5 + 19/x + 5 = 2/3
= 5 + x - 14/x + 5 = 2/3
= 15 + 3x - 42/2x + 10
= - 37 + 3x = 2x+10
= - 37 - 10 = 2x - 3x
= - 47 = - x
= 47 = x = His cousin age after 5 yrs=47 + 5 = 52yrs
= His age = 52 - 19 = 33yrs

Answer 2

Ⓖⓘⓥⓔⓝ :-

Raju is 19 years younger than his cousin.

ratios of their ages after 5 years = 2:3

Ⓕⓘⓝⓓ :-

THEIR PRESENT AGES ?

Ⓢⓞⓛⓤⓣⓘⓞⓝ  :-

Let age of cousin be x years

$\therefore$ Age of Raju = x-19 years

After 5 years

Age of cousin = x+5 years

Age of Raju = x - 19 + 5 = x - 14 years

ACCORDING TO QUESTION

$\frac{x - 14}{x + 5} = \frac{2}{3}$

$= 3 \times ( x - 14) = 2( x+ 5)$

$= > 3x - 42 = 2x + 10$

$collect \: like \: terms$

$= > 3x - 2x = 10 + 42$

$x = 52$

So, Present age of:

cousin = x = 52 years

Raju = x -19 = 52 - 19 = 33 years

$so, \: cousin \: present \: age \underline{ \boxed{52 \: years}}$

$and \: Raju\: present \: age \underline{ \boxed{33 \: years}}$