Question

Raju is 19 years younger than his cousin after 5 years their ages will be in the ratio 2:8 . find the present ages

please tell if you know

Answer 1

let present age of raju's cousin be x yrs
present age of raju=(x-19) yrs
after 5 yrs,
age of his cousin= x+5 yrs
age of raju =(x-19+5) yrs =x-14 yrs
ratio of their ages after 5 yrs = 2:8
let ages be 2y,8y
2y=x+5
y=(x+5)/2 ---eq1
x- 14=8y
(x-14)/8=y ----eq2
y=y
(x+5)/2=(x-14)/8
-(8*(x+5)=2*(x-14))
8x-40=2x-28
8x-2x=40-28
8x-2x=12
x=12/6=2

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

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

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