question_answer 19)

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

Answer:

                (a) 40 persons : 200 persons                 \[=\frac{40}{200}=\frac{40\div 10}{200\div 10}=\frac{4}{20}=\frac{1}{5}=1:5\] [dividing numerator and denominator both by 10] and  Rs. 15 : Rs. \[75=\frac{15}{75}=\frac{15\div 15}{75\div 15}=\frac{1}{5}=1:5\] [dividing numerator and denominator both by 15] Here, 1 : 5 = 1 : 5. So, given statement is true. (b) \[7.5L:15L=\frac{7.5}{15}=\frac{75}{150}\] [multiply numerator and denominator both by 10] \[=\frac{75\div 75}{150\div 75}=\frac{1}{2}=1:2\][\[\because \]HCF of 75 and 150 = 75] and 5 kg : 10 kg \[=\frac{5}{10}=\frac{5\div 5}{5\div 10}=\frac{1}{2}=1:2\] [\[\because \]HCF of 5 and 10 = 5] Here, 1 : 2 = 1 : 2. So, given statement is true. (c) \[99kg:45kg=\frac{99}{45}=\frac{99\div 9}{45\div 9}=\frac{11}{5}=11:5\]  [\[\because \]HCF of 99 and 45 = 9] and  Rs. 44 : Rs. \[20=\frac{44}{20}=\frac{44\div 4}{20\div 4}=\frac{11}{5}=11:5\]  [\[\because \]HCF of 44 and 20 = 4] Here, 11 : 5 = 11 : 5. So, given statement is true.                       (d) 32 m : 64 m\[=\frac{32}{64}=\frac{32\div 32}{64\div 32}=\frac{1}{2}=1:2\] [\[\because \] HCF of 32 and \[64=2\times 2\times 2\times 2\times \times 2=32\]] and 6s : 12 s\[=\frac{6}{12}=\frac{6\div 6}{12\div 6}=\frac{1}{2}=1:2\] [dividing numerator and denominator both by 6] Here, 1 : 2 = 1 : 2. So, given statement is true. (e) 45 km: 60 km\[=\frac{45}{60}=\frac{45\div 15}{60\div 15}=\frac{3}{4}=3:4\]   [\[\because \]HCF of 45 and 60 = 15] and 12 h : 15 h \[=\frac{12}{15}=\frac{12\div 3}{15\div 3}=\frac{4}{5}=4:5\] [\[\because \]HCF of 12 and 15 = 3] Here, \[3:4\ne 4:5.\] So, given statement is false.