Question

10years.hence a mans age will be twice the age of his son. Ten years ago man was 4times as old as his son. FIND THEIR PRESENT AGES????

Answer 1

Let present age of Man and his son be X and y Years respectively.




After 10 Years age of Man = ( X + 10 ) years.

And,

After 10 Years age of son = ( Y + 10 ) years.


According to the question,




2 ( Y + 10 ) = X + 10



2Y + 20 = X + 10



X - 2Y = 10 -----------(1)


Before 10 Years age of Man = ( X - 10 ) years.


And,

Before 10 years age of son = ( Y - 10 ) years.


According to the question,





4 ( Y - 10 ) = X - 10


4Y - 40 = X - 10



4Y - X = 30 ---------(2)




From equation (1) , we get

X - 2Y = 10



X = ( 10 + 2Y ) ----------(3)



Putting the value of X in equation (2) , we get


4Y - X = 30


4Y - ( 10 + 2Y ) = 30


4Y - 10 - 2Y = 30




2Y = 40


Y = 20 years


Putting the value of Y in equation (3) , we get



X = ( 10 + 2Y ) = 10 + 2 × 20 = 50 years.



Present age of son = Y = 20 years.



And,



Present age of Man = X = 50 years.

Answer 2

let age of man and son be X and y years.

a/q,

x + 10 = 2(y+10 )

x + 10 = 2y + 20

x - 2y = 10 -----(1)

and,

x - 10 = 4(y-10 )

x - 10 = 4y - 40

x - 4y = -30 -----(2)

on solving (1) and (2) , we get

x = 50 years and y = 20 years.