A) Each number is half of the sum
B) Each number is \[\frac{1}{3}\]and \[\frac{2}{3}\] respectively of the sum
C) Each number is \[\frac{1}{4}\] and \[\frac{3}{4}\] respectively of the sum
D) None of these
Correct Answer: A
Solution :
Suppose that two numbers are \[x\]and \[y\]. \[x+y=s\Rightarrow y=s-x\] Then \[f(x)=xy=x(s-x)=xs-{{x}^{2}}\] \[\therefore f'(x)=s-2x\] \[f'(x)=0\]for maximum value of \[f(x)\] \[\therefore x=\frac{s}{2}\] and \[y=\frac{s}{2}\] Thus each number is half of the sum.
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