Multiple choice

The ratio of the sum of the ages of two siblings, A and B, to the difference between their ages is 4 : 1. The ratio of the sum of the ages of B and C to the difference between their ages is 3 : 2. If A's age is the highest and C's age is the lowest, and the total of all their ages is 86 years, what is B's age?

  1. 15 years

  2. 25 years

  3. 30 years

  4. 40 years

  5. NA
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C be the ages. (A+B)/(A-B) = 4/1 implies A+B = 4A-4B, so 3A = 5B. (B+C)/(B-C) = 3/2 implies 2B+2C = 3B-3C, so B = 5C. Substituting B=5C into 3A=5B gives 3A=25C, so A = 25C/3. Total age A+B+C = 86 becomes (25C/3) + 5C + C = 86. Multiplying by 3 gives 25C + 15C + 3C = 258, so 43C = 258, C = 6. Then B = 5 * 6 = 30.

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