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Question

Find two numbers whose sum is 27 and product is 182.

A
12,15
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B
13,14
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C
11,16
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D
None of these
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Solution

The correct option is B 13,14
Let one number be x
Thus, the other number is 27x
Now, x(27x)=182
27xx2182=0
x227x+182=0
x214x13x+182=0
x(x14)13(x14)=0
(x14)(x13)=0
Thus, x14=0 or x13=0
x=14 or x=13
27x=2714=13 or 27x=2713=14
Therefore, the required numbers are 13,14.

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