Which of the following are four equivalent ratios of $\frac{1}{2}$ ?

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$\frac{2}{5}$ , $\frac{3}{5}$ , $\frac{4}{5}$ and $\frac{5}{15}$

$\frac{2}{4}$ , $\frac{3}{6}$ , $\frac{4}{8}$ and $\frac{5}{10}$

$\frac{2}{8}$ , $\frac{3}{12}$ , $\frac{4}{64}$ and $\frac{5}{100}$

$\frac{1}{4}$ , $\frac{1}{8}$ , $\frac{1}{16}$ and $\frac{1}{32}$

answer is A.

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Detailed Solution

Two ratios are said to be equivalent if any one of the ratios can be expressed as a multiple of the other. Some examples of equivalent ratios are 1:2 and 3:6, 4:5 and 12:15, etc.

Multiplying the numerator and denominator of $\frac{1}{2}$ , by 2,3,4 and 5 we get,

$\begin{matrix} \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \\ \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \\ \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \\ \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \end{matrix}$