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 present ages.

Answer 1

Given :-

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

To Find :-

Present ages

Solution :-

Let the present age of A and B be x and y respectively

According to the question

Five years ago

x - 5 = 4(y - 5)

x - 5 = 4y - 20

x - 4y = -20 + 5

x - 4y = -15 (i)

Five years after

x + 5 = 2(y + 5)

x + 5 = 2y + 10

x - 2y = 10 - 5

x - 2y = 5 (ii)

Subtract 1 from 2

x - 2y - x  4y = 5 - (-15)

-2y + 4y = 5 + 15

2y = 20

y = 20/2

y = 10

Using 2

x - 2(y) = 5

x - 2(10) = 5

x - 20 = 5

x = 20 + 5

x = 25

Hence

Age of A and B are 10 and 25 years respectively