Age word problem

Question

Juan is thrice as old as jose was when juan was as old as jose is now. When jose becomes twice as old as juan is now, together they will be 78 years. How old is jose now?

Answer 1

Let Juan's age be x and Jose's age be y

Juan was Jose's age x - y years ago.

At that time, Jose's age was y - (x - y) = 2y - x

Juan's age now is thrice Jose's age then, so

x = 3(2y - x)

x = 6y - 3x

4x = 6y

x = 3/2 y

Jose, now age y, becomes twice as old as Juan is now(2x) in 2x - y years

At that point, Juan's age is x + (2x - y) = 3x - y

The sum of their ages is 2x + 3x - y = 5x - y

As x = 3/2y

5x - y = 5(3/2y) - y = 15/2y - y = 13/2y

13/2y = 78

y = 78 *2/13 = 12

Jose's age is 12.