Question

10years ago Manish was 12times as old as his son and after 10years he will be twice as old as his son. Find their present ages.

Answer 1

HELLO DEAR FRIEND

Let the age of manish be x

and his son be y

ATQ,

(before 10 years)

x - 10 = 12(y - 10)

x - 10 = 12y - 120

x - 12y = -120 + 10

x - 12y = -110 ...(1)

also,

(after 10 years)

x + 10 = 2(y + 10)

x + 10 = 2y + 20

x - 2y = 20 - 10

x - 2y = 10 ...(2)

(1) - (2)

x - 12y - (x - 2y) = -110 - 10

x- 12y - x + 2y = -120

-10y = -120

$\large{ y = \frac{ \large{ - 120}}{ \large{ - 10}} }$

$\large \boxed{y = 12}$

putting the value of y on (2)

x - 2y = 10

x - 2(12) = 10

x - 24 = 10

x = 10 + 24

$\large \boxed{x = 34}$

so, the present age of Manish =

$\large{ \boxed{34 } \: years}$

and the present age of his son =

$\large{ \boxed{12 } \: years}$

THANKS