Q. X said to Y, “At the time of your birth I was twice as old as you are at present.” If the present age of X is 42 years, then consider the following statements:

1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.

Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Correct Answer: (b) 2 only

Explanation :

X & Y Age Relationship Analysis

Given:
– X’s present age = 42 years
– At Y’s birth, X was twice Y’s current age
– Let Y’s present age = y

Step 1: Initial Equation
– 42 – y = 2y (X’s age at Y’s birth = 2 × Y’s current age)
– 42 = 3y
– Therefore, y = 14 (Y’s current age)

Step 2: Testing Statement 1 (8 years ago)
– X’s age: 42 – 8 = 34
– Y’s age: 14 – 8 = 6
– Check: 34 ≠ 5 × 6 (30)
– Result: Statement 1 is false

Step 3: Testing Statement 2 (14 years later)
– X’s age: 42 + 14 = 56
– Y’s age: 14 + 14 = 28
– Check: 56 = 2 × 28
– Result: Statement 2 is true

Answer: Only Statement 2 is correct.