Multiple choice

A told B, When I was as old as you are now, then your age was four years less than half of my present age. If the sum of the present ages of A and B is 61 years, what is B's present age in years?

  1. 35

  2. 25

  3. 31

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A's age be x and B's age be y. When A was y, B was y - (x - y) = 2y - x. Given 2y - x = 0.5x - 4 and x + y = 61. From the first, 2y = 1.5x - 4, so y = 0.75x - 2. Substitute into the second: x + 0.75x - 2 = 61, 1.75x = 63, x = 36. Then y = 61 - 36 = 25.

AI explanation

Let A's and B's present ages be A and B respectively, with A being older than B. The age difference is A minus B, so when A was B's current age, the time elapsed was A minus B years ago, making B's age at that time 2B minus A. The statement gives 2B minus A equals (A divided by 2) minus 4, which simplifies to 4B minus 3A equals negative 8. The sum of their present ages is A plus B equals 61, so A equals 61 minus B. Substituting this into the first equation gives 4B minus 3 multiplied by (61 minus B) equals negative 8, which simplifies to 7B minus 183 equals negative 8, meaning 7B equals 175 and B equals 25.

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