Multiple choice

The present ages of A, B and C are in the ratio of 8 : 14 : 22, respectively. The present ages of B, C and D are in the ratio of 21 : 33 : 44, respectively. Which of the following represents the ratio of the present ages of A, B, C, and D, respectively?

  1. 12 : 21 : 33 : 44

  2. 12 : 22 : 31 : 44

  3. 12 : 21 : 36 : 44

  4. Cannot be determined

  5. None of these
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A Correct answer
Explanation

A:B = 8:14 = 4:7. B:C = 21:33 = 7:11. So A:B:C = 4:7:11. B:C:D = 21:33:44. To combine, multiply A:B:C by 3: 12:21:33. Now combine with B:C:D = 21:33:44. Result is 12:21:33:44.

AI explanation

To combine the ratios A:B:C = 8:14:22 and B:C:D = 21:33:44, equalize the common terms B and C by finding their combined ratio. The combined ratio of B and C is 42:66, which is obtained by multiplying the first ratio by 3 and the second by 2. This makes the overall ratio of A, B, C, and D equal to 24:42:66:88, which simplifies by dividing by 2 to 12:21:33:44.

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