Arrange the following ratios in ascending order of magnitude :
2 : 3, 17 : 21, 11 : 14 and 5 : 7.

Given, ratios are $\dfrac{2}{3}, \dfrac{17}{21}, \dfrac{11}{14}, \dfrac{5}{7}.$

We convert them into equivalent like fractions.

L.C.M. of 3, 21, 14, 7 = 42

$\dfrac{2}{3} = \dfrac{2 \times 14}{3 \times 14} = \dfrac{28}{42}, \\[0.5em] \dfrac{17}{21} = \dfrac{17 \times 2}{21 \times 2} = \dfrac{34}{42}, \\[0.5em] \dfrac{11}{14} = \dfrac{11 \times 3}{14 \times 3} = \dfrac{33}{42}, \\[0.5em] \dfrac{5}{7} = \dfrac{5 \times 6}{7 \times 6} = \dfrac{30}{42}. \\[0.5em]$

As, 28 < 30 < 33 < 34,

$\Rightarrow \dfrac{28}{42} \lt \dfrac{30}{42} \lt \dfrac{33}{42} \lt \dfrac{34}{42} \\[1em] \therefore \dfrac{2}{3} \lt \dfrac{5}{7} \lt \dfrac{11}{14} \lt \dfrac{17}{21}$

Hence, the given ratios in ascending order are 2 : 3, 5 : 7, 11 : 14, 17 : 21.