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…
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?
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Solution
Let Y's present age be y. At Y's birth X's age was $42 - y$, which equals twice Y's present age: $42 - y = 2y$, so $y = 14$. X is 42, Y is 14. Statement 1: 8 years ago ages were 34 and 6; 34 is not 5 times 6, so incorrect. Statement 2: after 14 years ages would be 56 and 28; 56 = 2 × 28, so correct. Hence option (b).