Question : If 45% of a certain number is equal to $\frac{6}{5}$th of another number, what is the ratio between the numbers?
Option 1: 9 : 11
Option 2: 8 : 3
Option 3: 1 : 7
Option 4: 7 : 4
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Correct Answer: 8 : 3
Solution : Let the first number as $x$ and the second number as $y$. According to the question, $\frac{45x}{100} = \frac{6y}{5}$ $⇒\frac{x}{y} = \frac{6×20}{5×9}$ $\therefore \frac{x}{y} = \frac{8}{3}$ Hence, the correct answer is 8 : 3.
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Question : The arrangement of the fractions $\frac{4}{3}, -\frac{2}{9}, -\frac{7}{8}, \frac{5}{12}$ in ascending order is _____.
Option 1: $–\frac{7}{8}, –\frac{2}{9}, \frac{5}{12}, \frac{4}{3}$
Option 2: $–\frac{7}{8}, –\frac{2}{9}, \frac{4}{3}, \frac{5}{12}$
Option 3: $–\frac{2}{9}, –\frac{7}{8}, \frac{5}{12}, \frac{4}{3}$
Option 4: $–\frac{2}{9}, –\frac{7}{8}, \frac{4}{3}, \frac{5}{12}$
Question : If $\left(3 y+\frac{3}{y}\right)=8$, then find the value of $\left(y^2+\frac{1}{y^2}\right)$.
Option 1: $5\frac{1}{9}$
Option 2: $4\frac{5}{6}$
Option 3: $7\frac{1}{9}$
Option 4: $9\frac{1}{9}$
Question : The next number of the sequence $\frac{1}{2},\frac{3}{4},\frac{5}{8},\frac{7}{16},........$ is:
Option 1: $\frac{10}{24}$
Option 2: $\frac{11}{32}$
Option 3: $\frac{9}{24}$
Option 4: $\frac{9}{32}$
Question : P, Q, and R are partners and invest in a business. P invests $\frac{1}{5}^{th}$ of total investments and Q invests $\frac{1}{4}^{th}$ of the total investments. What is the ratio of investments of P, Q, and R respectively?
Option 1: 4 : 8 : 11
Option 2: 4 : 5 : 11
Option 3: 4 : 7 : 11
Option 4: 4 : 5 : 9
Question : What is the difference between the largest and smallest of the given fractions? $\frac{5}{11}, \frac{5}{7}, \frac{3}{8}, \frac{6}{13}$
Option 1: $\frac{17}{56}$
Option 2: $\frac{19}{56}$
Option 3: $\frac{1}{ 7}$
Option 4: $\frac{23}{56}$
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