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?
2 only
Given:
X 's age was twice that of Y's present age when Y was born
Present age of X = 42 years
Calculation:
Let us assume present age of Y is y years.
So y years ago (time when Y was born), the age of X is twice of Y's present age
⇒ Age of X, y years ago = 42 - y
So the equation becomes 42 - y = 2y
⇒ y = 14
Present age of Y = 14 years
Statement 1
8 years ago, age of X = 42 - 8 = 34
age of Y = 14 - 8 = 6
Hence, statement 1 is wrong
Statement 2
14 years later, age of X = 42 + 14 = 56
age of Y = 14 + 14 = 28
Hence, statement 2 is correct.
Important Questions from Problem on Age
The ratio of present ages of Neelam and Rajni is 6 : 7. After four years, their ages will be in the ratio of 8 : 9. What is the present age of Rajni?
Five years ago the age of the son was one third of that of his mother at that time. If the sum of their present ages is 70 years, then find the present age of the mother.
Jaya is 36 years old and her son Bharat is 11 years old. In how many years will Jaya be twice as Bharat's age?
Five years ago, father's age was 5 times that of his son and after 3 years he will be 3 times as old as his son. Find the present age of son.
The ratio of a father's age to his son's age is 3 ∶ 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
