Question

Five years ago, A's age was four times the age of B. Five years hence, A’s age will be twice the age of B. Find their preset ages.

Answer 1

Let present age of A = x years

And present age of B = y years

According to the question,

Five years ago,

x - 5 = 4(y - 5)

x - 5 = 4y - 20

x - 4y = 5 - 20

x - 4y = -15                  ...(1)

Five years later,

x + 5 = 2(y + 5)

x + 5 = 2y + 10

x - 2y = 5                   ...(2)

Now subtracting (1) from (2)
x - 4y = -15
 x - 2y = 5 
  -    +     - 
-2y = -20

y = 10

From equation (1)

x - 4 (10) = -15

x = 25

Present ages of A and B are 25 years and 10 years respectively.