Multiple choice

The average age of A and B is 20 years. If C were to replace A, the average would be 19 and if C were to replace B, the average would be 21, what are the ratio of ages of A, B and C?

  1. 6 : 5 : 7

  2. 9 : 7 : 3

  3. 13 : 7 : 11

  4. 11 : 9 : 10
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let ages be A, B, C. (A+B)/2 = 20, so A+B = 40. (C+B)/2 = 19, so C+B = 38. (A+C)/2 = 21, so A+C = 42. From A+B=40 and C+B=38, subtracting: (A+B)-(C+B)=40-38, so A-C=2, or A=C+2. From A+C=42 and A=C+2: (C+2)+C=42, so 2C=40, C=20. Then A=22. From A+B=40: 22+B=40, B=18. So A:B:C = 22:18:20 = 11:9:10. Option D is correct.

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