X’s age 3 years ago was three times the present age of Y. At present Z’s age is twice the age of Y and also Z is 12 years younger than X. What is the present age of Z?

Question: X’s age 3 years ago was three times the present age of Y. At present Z’s age is twice the age of Y and also Z is 12 years younger than X. What is the present age of Z?

Solution:
Let,
Their present age is X, Y, Z respectively.

As X’s age 3 years ago was three times the present age of Y.
X - 3 = 3y
X - 3y = 3……….(i)

Z’s age is twice the age of Y
∴ Z = 2Y……….(ii)

Z is 12 years younger than X
∴ X - 12 = Z
Or, X - 12 = 2Y [ putting Z = 2Y from equation (ii) ]
Or, X - 2Y = 12……..(iii)

(iii) - (i),
X - 2Y - X + 3Y = 12 - 3
Or, Y = 9

So, the present age of Y is 9.
∴ the present age of Z is = 2Y = 2 x 9 = 18 years.