Question 987553
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<B>Answer</B>. &nbsp;40 and 50.


<B>Solution</B>


Let &nbsp;<B>x</B>&nbsp; be the smaller of the two parts.


Then the other part is &nbsp;90-x.


Notice that the sum of these parts is precisely &nbsp;90, &nbsp;while the difference is &nbsp;(90-x) - x = 90-2x.


Then, &nbsp;according to the condition,


{{{(90-2x)/90}}} = {{{1/9}}}, &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;----->


{{{90 - 2x}}} = {{{90/9}}},


90 - 2x = 10,


2x = 90 - 10 = 80,


x = {{{80/2}}} = 40.


Thus the smallest part is &nbsp;40, &nbsp;and the other part is &nbsp;90-40 = 50.