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?
Option 1: $\frac{4}{3}$
Option 2: $\frac{5}{4}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{5}$
Question : If the sum of a non-zero number and thrice its reciprocal is $\frac{52}{7}$. Find the number.
Option 1: 8
Option 2: 9
Option 3: 7
Option 4: 6
Question : What is the value of $\frac{\frac{5}{6} \text { of } \frac{1}{3} \times \frac{12}{25}-\frac{1}{3} \text { of } \frac{5}{6} \times \frac{18}{25}}{\frac{25}{12} \text { of } \frac{1}{6} \times \frac{2}{5}+\frac{3}{8} \text { of } \frac{12}{25} \times \frac{5}{6}}$?
Option 1: $-\frac{3}{13}$
Option 2: $-\frac{5}{13}$
Option 3: $-\frac{8}{25}$
Option 4: $-\frac{3}{25}$
Question : What is the value of $x$? $\frac{3}{2}× \frac{7}{3} ÷ \frac{7}{6}+\frac{1}{4}=\frac{1}{x}$
Option 1: $\frac{7}{12}$
Option 2: $\frac{4}{13}$
Option 3: $\frac{13}{4}$
Option 4: $\frac{6}{7}$
Question : What is the value of $\frac{\frac{5}{3} \text { of } \frac{1}{4} \times \frac{24}{5}-\frac{1}{5} \text { of } \frac{25}{8} \times \frac{24}{5}}{\frac{5}{12} \text { of } \frac{3}{4} \times \frac{4}{3}+\frac{3}{4} \text { of } \frac{12}{5} \times \frac{5}{6}}$?
Option 1: $-\frac{24}{23}$
Option 2: $-\frac{12}{23}$
Option 3: $-\frac{25}{46}$
Option 4: $-\frac{28}{23}$
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