MCQ
The two numbers whose sum is $27$ and their product is $182$ are :
- A$14$ and $15$
- B$12$ and $13$
- ✓$13$ and $14$
- D$12$ and $15$
✓
Answer
Correct option: C.
$13$ and $14$
Let the one number be $x.$
As the sum of numbers is $27,$ then the other number will be $(27 - x)$
According to question.
$x(27 - x) = 182$
$ \Rightarrow 27 x-x^2=182$
$ \Rightarrow x^2-27 x+182=0 $
$ \Rightarrow x^2-14 x-13 x+182=0 $
$\Rightarrow x(x - 14) -13(x - 14) = 0$
$\Rightarrow (x - 13) (x - 14) = 0$
$\Rightarrow x - 13 = 0$ and $x - 14 = 0$
$x = 13$ and $x = 14$
Now, the other number $= 27 - 13 = 14$ and $27 - 14 = 13$
$\therefore$ The required two numbers are $13$ and $14.$
As the sum of numbers is $27,$ then the other number will be $(27 - x)$
According to question.
$x(27 - x) = 182$
$ \Rightarrow 27 x-x^2=182$
$ \Rightarrow x^2-27 x+182=0 $
$ \Rightarrow x^2-14 x-13 x+182=0 $
$\Rightarrow x(x - 14) -13(x - 14) = 0$
$\Rightarrow (x - 13) (x - 14) = 0$
$\Rightarrow x - 13 = 0$ and $x - 14 = 0$
$x = 13$ and $x = 14$
Now, the other number $= 27 - 13 = 14$ and $27 - 14 = 13$
$\therefore$ The required two numbers are $13$ and $14.$
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