Question : Find the fraction which bears the same ratio to $\frac{1}{27}$ that $\frac{3}{7}$ does to $\frac{5}{9}$.
Option 1: $\frac{5}{9}$
Option 2: $\frac{1}{35}$
Option 3: $\frac{45}{7}$
Option 4: $\frac{7}{45}$
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Correct Answer: $\frac{1}{35}$
Solution : Let the required fraction be $x$. As per the question, $\frac{x}{\frac{1}{27}}=\frac{\frac{3}{7}}{\frac{5}{9}}$ ⇒ $27x=\frac{27}{35}$ $\therefore x=\frac{1}{35}$ Hence, the correct answer is $\frac{1}{35}$.
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Question : Which fraction among the following is the least? $\frac{5}{11}, \frac{7}{12}, \frac{8}{13}, \frac{9}{17}$
Option 1: $\frac{5}{11}$
Option 2: $\frac{7}{12}$
Option 3: $\frac{9}{17}$
Option 4: $\frac{8}{13}$
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:
Option 1: $\frac{5}{8}$
Option 2: $\frac{3}{4}$
Option 3: $\frac{5}{6}$
Option 4: $\frac{3}{7}$
Question : A fraction is greater than its reciprocal by $\frac{9}{20}$. What is the fraction?
Option 1: $\frac{5}{4}$
Option 2: $\frac{4}{5}$
Option 3: $\frac{3}{4}$
Option 4: $\frac{4}{3}$
Question : Choose the option in which the numbers are in the correct ascending order.
Option 1: $\frac{4}{5}, \frac{2}{3}, \frac{1}{11}$ and $\frac{2}{9}$
Option 2: $\frac{1}{11}, \frac{2}{9}, \frac{2}{3}$ and $\frac{4}{5}$
Option 3: $\frac{2}{9}, \frac{1}{11}, \frac{4}{5}$ and $\frac{2}{3}$
Option 4: $\frac{2}{3}, \frac{4}{5}, \frac{1}{11}$ and $\frac{2}{9}$
Question : A fraction is greater than twice its reciprocal by $\frac{7}{15}$. What is the fraction?
Option 1: $\frac{3}{5}$
Option 2: $\frac{5}{3}$
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