Question

Ramesh is 19 years younger than his father. After 5 years, their ages will be in the ratio of 2:3 find their present ages​

Answer 1

Answer

LET THE RAMESH AGE BE = X

AND FATHER AGE BE = X+19

5 YEAR LATER RAMESH AGE BE = X+5

AND FATHER AGE BE = X+19+5 = X+24

AGES IN RATIO = 2:3SO........ X+5 : X+24 :: 2:3

》2(X+24) = 3(X+2)

》2X + 48 = 3X + 15

》2X - 3X = 15 - 48

》-X = -33

》X = 33

Answer 2

GIVEN:-

Ramesh 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 Ramesh = x-19 years

After 5 years

Age of Father = x+5 years

Age of Ramesh = 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

Ramesh = x -19 = 52 - 19 = 33 years

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

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