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

Question

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?

Accepted Answer

Let X's present age be X and Y's present age be Y.
Given, present age of X = 42 years.

From the statement: "At the time of your birth I was twice as old as you are at present."
At the time of Y's birth, Y's age was 0.
X's age at Y's birth was X - Y (current age of X minus Y's current age).
So, X - Y = 2 * Y
X = 3Y

Substitute the present age of X (42 years):
42 = 3Y
Y = 42 / 3
Y = 14 years.
So, present age of X = 42 years, and present age of Y = 14 years.

Now let's evaluate the statements:

Statement 1: "8 years ago, the age of X was five times the age of Y."
8 years ago:
Age of X = 42 - 8 = 34 years.
Age of Y = 14 - 8 = 6 years.
Is 34 = 5 * 6?
34 = 30. This is false.
So, Statement 1 is incorrect.

Statement 2: "After 14 years, the age of X would be two times the age of Y."
After 14 years:
Age of X = 42 + 14 = 56 years.
Age of Y = 14 + 14 = 28 years.
Would 56 = 2 * 28?
56 = 56. This is true.
So, Statement 2 is correct.

Therefore, only Statement 2 is correct.

The final answer is B) 2 only.

Answer

1 only

Answer

2 only

Answer

Both 1 and 2

Answer

Neither 1 nor 2

Explanation

Related questions