Question

lucky's is 19 year younger than his father after 5 years year their age will be in the ratio of 2:3 find a present ages​

Answer 1

Let the present age of Lucky's father be,

x years.

Then the present age of Lucky will be ,

(x-19) years.

Also,

Lucky's father's age after 5 years will be,

(x+5) years

Lucky's age after 5 years will be;

(x-19+5) years ,ie; (x-14) years.

According to the question;

After five years, the ratio of Lucky's age and his father's age will be 2:3.

=> (x-14):(x+5) = 2:3

=> (x-14)/(x+5) = 2/3

=> 3(x-14) = 2(x+5)

=> 3x - 42 = 2x + 10

=> 3x - 2x = 10 + 42

=> x = 52

Hence,

The present age of Lucky's Father is :

x years , ie; 52 years.

Also,

The present age of Lucky is :

(x-19) years , ie; (52-19) years

ie; 33 years.

Answer 2

GIVEN:-

Lucky is 19 years younger than his Father.

ratios of their ages after 5 years = 2:3

FIND:-

THEIR PRESENT AGES ?

SOLUTION:-

Let age of Father be x years

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

After 5 years

Age of Father = x+5 years

Age of Lucky = 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:

Father = x = 52 years

Lucky = x -19 = 52 - 19 = 33 years

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

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