Question : The sum of a fraction and 4 times its reciprocal is $\frac{13}{3}$. What is the fraction?
Option 1: $\frac{4}{3}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{5}{4}$
Option 4: $\frac{4}{5}$
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Correct Answer: $\frac{4}{3}$
Solution : Let the fraction be $a$. Given: $a + \frac{4}{a} = \frac{13}{3}$ After solving this, we get $({a}^{2} + {4}) × 3 = 13a$ $3{a}^{2} -13a + 12 = 0$ $3{a}^{2} -9a -4a+ 12 = 0$ $3{a}(a-3) -4(a - 3) = 0$ $(a-3)(3a - 4) = 0$ $(a-3)=0$ or $(3a - 4) = 0$ ⇒ $a = 3, \frac{4}{3}$ So, the fraction = $\frac{4}{3}$ Hence, the correct answer is $\frac{4}{3}$.
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Question : A fraction is greater than its reciprocal by $\frac{9}{20}$. What is the fraction?
Question : A fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?
Question : The smallest fraction which should be added to the sum of $2\frac{1}{2}, 3\frac{1}{3}, 4\frac{1}{4}$ and $5\frac{1}{5}$ to make the result a whole number is:
Question : Let $x=\frac{5 \frac{3}{4}-\frac{3}{7} \times 15 \frac{3}{4}+2 \frac{2}{35} \div 1 \frac{11}{25}}{\frac{3}{4} \div 5 \frac{1}{4}+5 \frac{3}{5} \div 3 \frac{4}{15}}$. When $y$ is added to $x$, the result is $\frac{7}{13}$. What is the value of $y$?
Question : The sum of three fractions is $2\frac{11}{24}$. On dividing the largest faction by the smallest fraction, $\frac{7}{6}$ is obtained which is $\frac{1}{3}$ greater than the middle fraction. The smallest fraction is:
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