UPSC Prelims 2021·CSAT·Quantitative Aptitude·Arithmetic

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?

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  1. A1 only
  2. B2 onlyCorrect
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Explanation

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.
Quantitative Aptitude: 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,
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