Question

.6 years hence, a man's age will be 3 times the age of his son and three years ago he was nine times as old as his son. The present age of the man is -Immersive Reader

Answer 1

ANSWER

Let the age of man be x

and the age of his son be y

According to the question:

After 6 years :  

(x+6)=3(y+6)

⇒x−3y=12⟶(i)

Three years ago :

x−3=9(y−3)

⇒x−3=9y−27

⇒x−9y=−24⟶(ii)

Solving (i) and (ii),  

6y=36

⇒y=6

Putting value of y in equation (i),

x−3xy=12

∴x=12+18

x=30

∴ Age of man =30 years.

  Age of son =6 years.

OR FOR MORE DESCRIBED SOLVING PLEASE CHECK THE BELOW SOLUTION...

let the age of the man be x and his son be y (in years)

Then ATQ,

(x + 6) = 3(y + 6)

=> x + 6 = 3y = 18

=> x - 3y = 12 ------- (1)

Also

(x - 3) = 9(y - 3)

=> x - 3 = 9y - 27

=> x - 9y = -24 -------(2)

Subtract (2) from (1)

=> x - 3y - (x - 9y) = 12 -(-24)

=> 6y = 36

=> y = 6 years.

Thus using y in (1)

=> x - 3(6) = 12

=> x = 30 years

Thus Father's age is 30 years and son's age is 6 years.