Question

Five years ago A was thrice as old as B and 10 years later A will be twice as old as B. The age of B is:

Answer 1

Let the age of A be x
and B be y

Five years ago

A's age :- x - 5

B's age :- y - 5

x - 5 = 3 ( y - 5 )

x - 5 = 3y - 15

x - 3y = - 15 + 5

x - 3y = - 10

x = 3y - 10 ......( i )


After 10 years

A's age :- x + 10
B's age :- y + 10


x + 10 = 2 ( y + 10 )

x + 10 = 2y + 20

x - 2y + 10 - 20 = 0

x - 2y - 10 = 0 ..... ( ii )


Putting the value of x from ( i ) in ( ii )

x - 2y - 10 = 0

3y - 10 - 2y - 10 = 0

y - 20 = 0

y = 20

Putting in ( i )

x = 3y - 10

x = 60 - 10

x = 50

A's age is 50 years
B's age is 20 years.