The sum of three numbers is 98. If the ratio of the first to second is 2 :3…

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The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:

  1. A.

    20

  2. B.

    30

  3. C.

    48

  4. D.

    58

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Correct answer: B

Let the three numbers be A, B, C.

  1. From A:B = 2:3, write A = 2x and B = 3x.

  2. From B:C = 5:8, write B = 5y and C = 8y.

  3. Equate B: 3x = 5y ⇒ x = 5y/3. Substitute to get A = 2x = 10y/3, B = 3x = 5y, C = 8y.

  4. Clear the fraction by multiplying by 3: A:B:C = 10:15:24.

  5. Total parts = 10 + 15 + 24 = 49. Each part = 98/49 = 2, so the second number = 15 × 2 = 30.

Answer: 30

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