Question : The sum of twice a number and thrice its reciprocal is $\frac{25}{2}$. What is the number?
Option 1: 7
Option 2: 6
Option 3: 5
Option 4: 4
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Correct Answer: 6
Solution :
Given: The sum of a twice a number and thrice its reciprocal is $\frac{25}{2}$.
Let the number be $x$.
According to the question,
$2x+\frac{3}{x}=\frac{25}{2}$
$\Rightarrow 4x^2+6=25x$
$\Rightarrow 4x^2-25x+6=0$
$\Rightarrow 4x^2-24x-x+6=0$
$\Rightarrow (4x-1)(x-6)=0$
$\Rightarrow (4x-1)=0$ or $(x-6)=0$
$\Rightarrow x=6$ or $\frac{1}{4}$
After checking the options, we get, $x=6$
Hence, the correct answer is 6.
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