Question

Which of the following ratios is in proportion?

• A. 2 : 6 :: 4 : 8
• B. 6 : 12 :: 5 : 10
• C. 5 : 20 :: 4 : 24
• D. 3 : 12 :: 7 : 21

Answer 1

The correct option is B 6 : 12 :: 5 : 10

If the simplest form of two ratio is same, they are said to be in proportion.
a) $\frac{2}{6}$ = $\frac{1}{3}$ × $\frac{2}{2}$ and $\frac{4}{8}$ = $\frac{1}{2}$ × $\frac{4}{4}$
∵ $\frac{1}{3}$ ≠ $\frac{1}{2}$, thus, $\frac{2}{6}$ and $\frac{4}{8}$ are not in proportion.
b) $\frac{6}{12}$ = $\frac{1}{2}$ × $\frac{6}{6}$ and $\frac{5}{10}$ = $\frac{1}{2}$ × $\frac{5}{5}$
∵ $\frac{1}{2}$ = $\frac{1}{2}$, thus, $\frac{6}{12}$ and $\frac{5}{10}$ are in proportion.
c) $\frac{5}{20}$ = $\frac{1}{4}$ × $\frac{5}{5}$ and $\frac{4}{24}$ = $\frac{1}{6}$ × $\frac{4}{4}$
∵ $\frac{1}{4}$ ≠ $\frac{1}{6}$, thus, $\frac{2}{6}$ and $\frac{4}{8}$ are not in proportion.
d) $\frac{3}{12}$ = $\frac{1}{4}$ × $\frac{3}{3}$ and $\frac{7}{21}$ = $\frac{1}{3}$ × $\frac{7}{21}$
∵ $\frac{1}{4}$ ≠ $\frac{1}{3}$, thus, $\frac{3}{12}$ and $\frac{7}{21}$ are not in proportion.