Multiple choice

A man had three daughters who celebrated their birthday on the same day, but were born in 1977, 1978 and 1979. On one such birthday, if the product of their ages was divided by their respective ages in turn, the sum of quotients would have been 74. Find the age of the eldest daughter (in years).

  1. 6

  2. 8

  3. 9

  4. None of these
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A Correct answer
Explanation

Let ages be x, x+1, x+2. Product P = x(x+1)(x+2). Sum of quotients = P/x + P/(x+1) + P/(x+2) = (x+1)(x+2) + x(x+2) + x(x+1) = 74. x^2+3x+2 + x^2+2x + x^2+x = 74 => 3x^2 + 6x - 72 = 0 => x^2 + 2x - 24 = 0 => (x+6)(x-4) = 0. x = 4. Eldest is 4+2 = 6.

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