Arrange the following ratios in ascending order of magnitudes :

(i) (4 : 9), (6 : 11), (7 : 13) and (27 : 50)

(ii) (2 : 3), (8 : 15), (11 : 12) and (7 : 16)

(iii) (3 : 5), (4 : 9), (5 : 11) and (10 : 17)

(i) Given,

(4 : 9), (6 : 11), (7 : 13) and (27 : 50)

We convert them into decimals.

⇒ $\dfrac{4}{9}$ ≈ 0.444

⇒ $\dfrac{6}{11}$ ≈ 0.5455

⇒ $\dfrac{7}{13}$ ≈ 0.5385

⇒ $\dfrac{27}{50}$ ≈ 0.5400

⇒ 0.444 < 0.5385 < 0.5400 < 0.5455

⇒ (4 : 9) < (7 : 13) < (27 : 50) < (6 : 11).

Hence, the ratios in ascending order are (4 : 9), (7 : 13), (27 : 50), (6 : 11).

(ii) Given,

(2 : 3), (8 : 15), (11 : 12) and (7 : 16)

We convert them into decimals.

$\dfrac{2}{3}$ = 0.667

$\dfrac{8}{15}$ ≈ 0.533

$\dfrac{11}{12}$ ≈ 0.917

$\dfrac{7}{16}$ = 0.4375

0.4375 < 0.533 < 0.667 < 0.917

(7 : 16) < (8 : 15) < (2 : 3) < (11 : 12)

Hence, the ratios in ascending order are (7 : 16), (8 : 15), (2 : 3), (11 : 12).

(iii) Given,

(3 : 5), (4 : 9), (5 : 11) and (10 : 17)

We convert them into decimals.

$\dfrac{3}{5}$ = 0.600

$\dfrac{4}{9}$ ≈ 0.444

$\dfrac{5}{11}$ ≈ 0.455

$\dfrac{10}{17}$ = 0.588

⇒ 0.444 < 0.455 < 0.588 < 0.600

⇒ (4 : 9) < (5 : 11) < (10 : 17) < (3 : 5)

Hence, the ratios in ascending order are (4 : 9), (5 : 11), (10 : 17), (3 : 5).