Question

Rahul is 19 years younger than his cousin. After 5 years ,their ages will be in the ratio 2:3. Find thei r present ages.

Answer 1

R = C-19

3(R+5) = 2(C+5)

3(C-19+5) = 3C - 42 = 2C+10

C=52

R = 52 - 19 = 33

Answer 2

Ⓖⓘⓥⓔⓝ :-

Rahul 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 Rahul = 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

Rahul = x -19 = 52 - 19 = 33 years

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

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