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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Question : The sum of twice a fraction and its reciprocal is $\frac{17}{6}$. What is the fraction?
Question : If the sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Find the number.
Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?
Question : A positive number is greater than thrice its reciprocal by $\frac{26}{3}$. What is the number?
Question : What is the value of $\frac{\frac{5}{12} \text { of } \frac{6}{25}-\frac{5}{6} \times \frac{12}{33}+\frac{5}{11} \div \frac{25}{33}}{\frac{1}{6} \div \frac{1}{2}+\frac{1}{6} \times \frac{1}{2}-\frac{1}{2} \text { of } \frac{1}{6}}$?
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