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Question
50 is divided into two parts such that the sum of their reciprocals is 1/12. Find the two parts.
30 and 20
30 and 25
30 and 40
30 and 35
ANSWER : 1
Descrption
<p>Hints: Look at the answer, only A has 30 and 20, 30 + 20 = 50, which is the answer.</p> <p>Alternatively, let the two parts be x, y ; so x + y = 50 </p> <p>1/x + 1/y = 1/12</p> <p>(y + x)/xy = 1/12</p> <p>50 /xy = 1/12</p> <p>xy = 600</p> <p>x( 50 - x) = 600</p> <p>50x - x<sup>2</sup> = 600</p> <p>x<sup>2</sup> - 50x + 600 = 0 </p> <p>(x - 30) (x - 20) = 0</p> <p>x = 30, 20 </p>
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