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Question

Find the two positive numbers x & y such that their sum is 60 and xy3 is maximum

A
15 & 45
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B
30 & 30
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C
20 & 40
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D
10 & 50
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Solution

The correct option is C 15 & 45
Let one number be x
Hence the other number will be (60x).
Let
K=x3.(60x)
Differentiating K with respect to x, we get
dKdx
=3x2(60x)x3=0
Or
x2[1803xx]=0
Or
x=0 and x=1804=45.
Now its given that the numbers are positive.
Hence x=0 is ruled out.
Thus we get x=45.
Hence
y=15.
Therefore the numbers are 45,15.

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