Question

Are the following statements true?
(a) 40 persons: 200 persons = ₹15: ₹75
(b) 7.5 litres : 15 litres = 5 kg: 10 kg
(c) 99 kg: 45 kg = ₹ 44: ₹20
(d) 32 m: 64 m = 6 sec: 12 sec
(e) 45 km: 60 km = 12 hours: 15 hours

Answer 1

(a) 40 persons: 200 persons = \(₹15: ₹ 75\)
\(= \frac{40}{200} = \frac{1}{5} = 1:5\)

\(₹ 15: ₹ 75 = \frac{15}{75}\)
\(=\frac{ 1}{5}\)
\(= 1:5\)
Since, 40 persons: 200 persons \(= ₹ 15 : ₹ 75\)
Hence, the statement is true.

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(b) 7.5 litres : 15 litres = 5kg: 10kg
\(=\frac{ 7.5}{15} = \frac{75}{150}\)

\(= \frac{1}{2} = 1:2\)
5 kg: 10 kg = \(\frac{5}{10}\)
\(= \frac{1}{2} = 1:2\)
Since, 7.5 liters: 15 liters = 5 kg: 10 kg
Hence, the statement is true. 

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(c) 99 kg: 45kg = \(₹44 :₹20\)
\(= \frac{99}{45} = \frac{11}{5}\)
\(= 11:5\)
\(₹ 44 : ₹ 20 = \frac{44}{20}\)
\(= \frac{11}{5} = 11:5\)
Since, 99 kg: 45 kg\(= ₹ 44 : ₹ 20\)
Hence, the statement is true. 

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(d) 32m: 64m=6sec: 12 sec
\(= \frac{32}{64} = \frac{1}{2} = 1:2\)

6 sec: 12 sec =\(\frac{ 6}{12}\)
\(= \frac{1}{2} = 1:2\)
Since, 32 m: 64 m = 6 sec: 12 sec
Hence, the statement is true.

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 (e) 45km: 60km = 12hours: 15 hours
\(= \frac{45}{60} = \frac{3}{4} = 3:4\)

12 hours: 15 hours \(= \frac{12}{15} =\frac{ 4}{5} = 4:5\)
Since, 45 km: 60 km \(≠\) 12 hours : 15 hours
Hence, the statement is false.

So, the answers is: (a) True (b) True (c) True (d) True (e) False