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# The sum of the reciprocal of the ages of two sisters is five

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The sum of the reciprocal of the ages of two sisters is five [#permalink]  29 Feb 2004, 15:58
The sum of the reciprocal of the ages of two sisters is five times the difference of the reciprocal of their ages. If the ratio of the product of their ages to that of the sum of their ages is 12:1, what is the age of the elder sister?

20
25
30
40
45
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C for me

Let X = age of older sister
Let Y = age of younger sister

From 1) 1/X + 1/Y = 5(1/Y - 1/X) --> We have to take reciprocal of age of younger sister minus reciprocal of age of older sister in order to have a positive difference
From 2) XY / (X + Y) = 12 --> XY = 12X + 12Y --> X = 12X/Y + 12

We can simplify first stem to: 1/X + 1/Y = 5/Y - 5/X --> 6/X = 4/Y --> Y = 2X/3

Plug this in second stem: X = [12X / (2X/3)] + 12 = 18 + 12 = 30
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