Multiple choice

The sum of the ages of A, B, and C is 120 years. The difference between the ages of A & B is three times the difference between the ages of B & C. If the ratio of the age of B to that of C is 8 : 5, then what is the minimum possible age of A (in years)? (Given that age of A > age of B and all ages are integers)

  1. 68

  2. 45

  3. 54

  4. 86

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A+B+C=120. B/C = 8/5, so B=8k, C=5k. A-B = 3(B-C) => A-8k = 3(8k-5k) = 9k => A=17k. A+B+C = 17k+8k+5k = 30k = 120, so k=4. A=68, B=32, C=20. Condition A>B is satisfied. Minimum age of A is 68.

AI explanation

Given the ratio of B to C is 8 to 5, let B equal 8x and C equal 5x; the difference between their ages is 3x. The difference between A and B is three times the difference between B and C, so A minus B equals 9x, and since A is older, A equals 8x plus 9x, which is 17x. The sum of their ages is 120, so 17x plus 8x plus 5x equals 120, meaning 30x equals 120 and x equals 4. To find the minimum integer age of A, x must be an integer, making the minimum value for x equal to 4, so A is 17 times 4, which is 68.

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