Question

Raju is 19 years younger than his cousin. After 5 years their ages will be in the ratio 2:8. Find their parents ages.

Answer 1

Let his cousin be x years old and Raju would be x.- 19 yrs old.
After 5 years their ages in Ratio = 2:8
Therefore;
Raju = ( X-19 +5) :His cousin = X +5 ::2:8
X-19+5 : X+5 :: 2:8
X-14/X +5 = 2/8
8(X-14) = 2(X+5)
8X - 112 = 2X +10
8X -2X = 10 +112
6X =122
X = 122/6
X = 21.
Therefore after 5 years
His cousin = 21 +5 =26 years old.
Raju = 21 - 19 =2+5 =7 yrs old

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

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

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