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Introduction to Proportions

Write 'T' for...

Question

Write 'T' for true and 'F' for false for each of the statements given below:
(i) 30, 40, 45, 60 are in proportion.
(ii) 6 : 8 and 9 : 12 are equivalent ratios of 3 : 4.
(iii) a dozen : a score = 5 : 3.
(iv) 60 p : Rs 3 = 1 : 5.

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Solution

(i) 30, 40, 45, 60
30 = 3 , 45 = 45 ÷ 15 = 3 They are in proportion.
40 4 60 60 ÷ 15 4
Hence, true.

(ii) 6 = 6 ÷ 2 = 3 , 9 = 9 ÷ 3 = 3 Hence, they are equivalent to 3:4.
8 8 ÷ 2 4 2 12 ÷ 3 4
Hence, true.
(iii) 1 dozen:1 score = 12:20
12 = 12 ÷ 4 = 3
20 20 ÷ 4 5
Hence, false.
(iv) 60p:Rs 3 = 60p:300p (1 Re = 100 p)
60 = 6 = 6 ÷ 6 = 1
300 30 30 ÷ 6 5

Hence, true.

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