Question

Write the ratio of first quantity to second quantity in the reduced form.

(i) 1024 MB, 1.2 GB [(1024 MB = 1 GB)] (ii) 17 Rupees, 25 Rupees 60 paise (iii) 5 dozen, 120 units

(iv) 4 sq.m, 800 sq.cm (v) 1.5 kg, 2500 gm

Answer 1

(i)
Ratio of 1024 MB to 1.2 GB

= 1024 MB : 1.2 × 1024 MB

$$\begin{gathered} =\frac{1024}{1.2\times 1024} \\ =\frac{1}{1.2} \\ =\frac{10}{12} \\ =\frac{5}{6} \end{gathered}$$
= 5 : 6

(ii)
17 Rupees = 1700 paise (Re 1 = 100 paise)

25 Rupees 60 paise = 25 Rupees + 60 paise = 2500 paise + 60 paise = 2560 paise

∴ Ratio of 17 Rupees to 25 Rupees 60 paise

= 1700 paise : 2560 paise

$$\begin{gathered} =\frac{1700}{2560} \\ =\frac{1700÷20}{2560÷20}\left(\mathrm{HCF}\mathrm{of}1700\mathrm{and}2560=20\right) \\ =\frac{85}{128} \end{gathered}$$
= 85 : 128

(iii)
Ratio of 5 dozen to 120 units

= 5 × 12 units : 120 units

= 60 units : 120 units

$$\begin{gathered} =\frac{60}{120} \\ =\frac{1}{2} \end{gathered}$$
= 1 : 2

(iv)
1 m² = 10000 cm²

4 m² = 4 × 10000 cm² = 40000 cm²

∴ Ratio of 4 m² to 800 cm²

= 40000 cm² : 800 cm²

$$\begin{gathered} =\frac{40000}{800} \\ =50 \end{gathered}$$
= 50 : 1

(v)
1.5 kg = 1.5 × 1000 g = 1500 g

∴ Ratio of 1.5 kg to 2500 g

= 1500 g : 2500 g

$$\begin{gathered} =\frac{1500}{2500} \\ =\frac{3}{5} \end{gathered}$$
= 3 : 5