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Question
Determine if the following ratios form a proportion:
(i) 25 cm : 1 m and Rs 40 : Rs 160
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
(iii) 200 mL : 2.5 L and Rs 4 : Rs 50
(iv) 2 kg : 80 kg and 25 g : 625 kg
(i) 25 cm : 1 m and Rs 40 : Rs 160
(ii) 39 litres : 65 litres and 6 bottles : 10 bottles
(iii) 200 mL : 2.5 L and Rs 4 : Rs 50
(iv) 2 kg : 80 kg and 25 g : 625 kg
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Solution
(i) 25 cm:1 m and Rs 40:Rs 160 (or) 25 cm:100 cm and Rs 40:Rs 160
25 = 25 ÷ 25 = 1 and 40 = 40 ÷ 40 = 1
100 100 ÷ 25 4 160 160 ÷ 40 4
Hence, they are in proportion.
(ii) 39 litres:65 litres and 6 bottles:10 bottles
39 = 39 ÷ 13 = 3 and 6 = 6 ÷ 2 = 3
65 65 ÷ 13 5 10 10 ÷ 2 5
Hence they are in proportion.
(iii) 200 mL:2.5 L and Rs 4:Rs 50 (or) 200 mL:2500 mL and Rs 4:Rs 50
200 = 2 and 4 = 4 ÷ 2 = 2
2500 25 50 50 ÷ 2 25
Hence, they are in proportion.
(iv) 2 kg:80 kg and 25 g:625 kg (or) 2 kg:80 kg and 25 g:625000 g
2 = 2 ÷ 2 = 1 and 25 = 25 ÷ 25 = 1
80 80 ÷ 2 40 625000 625000 ÷ 25 25000
Hence, they are not in proportion.
25 = 25 ÷ 25 = 1 and 40 = 40 ÷ 40 = 1
100 100 ÷ 25 4 160 160 ÷ 40 4
Hence, they are in proportion.
(ii) 39 litres:65 litres and 6 bottles:10 bottles
39 = 39 ÷ 13 = 3 and 6 = 6 ÷ 2 = 3
65 65 ÷ 13 5 10 10 ÷ 2 5
Hence they are in proportion.
(iii) 200 mL:2.5 L and Rs 4:Rs 50 (or) 200 mL:2500 mL and Rs 4:Rs 50
200 = 2 and 4 = 4 ÷ 2 = 2
2500 25 50 50 ÷ 2 25
Hence, they are in proportion.
(iv) 2 kg:80 kg and 25 g:625 kg (or) 2 kg:80 kg and 25 g:625000 g
2 = 2 ÷ 2 = 1 and 25 = 25 ÷ 25 = 1
80 80 ÷ 2 40 625000 625000 ÷ 25 25000
Hence, they are not in proportion.
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