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Q.3 Are the following statements true?
(a) 40 persons : 200 persons = Rs 15 : Rs 75
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
(c) 99 kg : 45 kg = Rs 44 : Rs 20
(d) 32 m : 64 m = 6 sec : 12 sec
(e) 45 km : 60 km = 12 hours : 15 hours
Answer :

(a) 40 persons : 200 persons = Rs 15 : Rs 75
\(\frac{40}{200} = \frac{1}{5} \)
\(\frac{15}{75} = \frac{1}{5} \)
Hence, True
(b) 7.5 litres : 15 litres = 5 kg : 10 kg
\(\frac{7.5}{15} = \frac{1}{2} \)
\(\frac{5}{10} = \frac{1}{2} \)
Hence, True
(c) 99 kg : 45 kg = Rs 44 : Rs 20
\(\frac{99}{45} = \frac{11}{5} \)
\(\frac{44}{20} = \frac{11}{5} \)
Hence, True
(d) 32 m : 64 m = 6 sec : 12 sec
\(\frac{32}{64} = \frac{1}{2} \)
\(\frac{6}{12} = \frac{1}{2} \)
Hence, True
(e) 45 km : 60 km = 12 hours : 15 hours
\(\frac{45}{60} = \frac{3}{4} \)
\(\frac{12}{15} = \frac{4}{5} \)
Hence, False

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