Multiple choice

$10$ years before, the ratio of ages of $A$ and $B$ was $13:17$. After $17$ years from now, the ratio of their ages will be $10:11$. The present age $B$ is

  1. $23\ years$
  2. $40\ years$
  3. $27\ years$
  4. $44\ years$
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C Correct answer
Explanation

Let A and B be current ages. (A-10)/(B-10) = 13/17 => 17A - 170 = 13B - 130 => 17A - 13B = 40. (A+17)/(B+17) = 10/11 => 11A + 187 = 10B + 170 => 10B - 11A = 17. Solving this system gives B = 27.

AI explanation

Let the present ages of A and B be x and y. Ten years ago, the equation is (x minus 10) divided by (y minus 10) equals 13 divided by 17, which simplifies to 17x minus 13y equals 40. Seventeen years from now, the equation is (x plus 17) divided by (y plus 17) equals 10 divided by 11, simplifying to 11x minus 10y equals 17. Solving this system of linear equations yields x equals 23 and y equals 27. Therefore, the present age of B is 27 years.

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