Answer:
(a) We have, 16 : 24 : : 20 : 30 \[\therefore \]Ratio of 16 to \[24=\frac{16}{24}=\frac{16\div 8}{24\div 8}=\frac{2}{3}=2:3\] [\[\because \]HCF of 16 and \[24=2\times 2\times 2=8\]] and ratio of 20 to \[30=\frac{20}{30}=\frac{20\div 10}{30\div 10}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 10] Here, 16 : 24 = 20 : 30 = 2 : 3, so 16 : 24 :: 20 : 30 Hence, given statement is true. (b) We have, 21 : 6 : : 35 : 10 Ratio of 21 to \[6=\frac{21}{6}=\frac{21\div 3}{6\div 3}=\frac{7}{2}=7:2\] [dividing numerator and denominator both by 3] and ratio of 35 to \[10=\frac{35}{10}=\frac{35\div 5}{10\div 5}=\frac{7}{2}=7:2\] [dividing numerator and denominator both by 5] Here, 21 : 6 = 35 : 10 = 7 : 2, so 21 : 6 : : 35 : 10 Hence, given statement is true. (c) We have, 12 : 18 : : 28 : 12 \[\therefore \] Ratio of 12 to\[18=\frac{12}{18}=\frac{12\div 6}{18\div 6}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 6] and ratio of 28 to \[12=\frac{28}{12}=\frac{28\div 4}{12\div 4}=\frac{7}{3}=7:3\] [dividing numerator and denominator both by 4] Here, \[2:3\ne 7:3\]i.e.\[12:18\ne 28:12\] Hence, given statement is false. (d) We have, 8 : 9 : : 24 : 27 Ratio of 8 to \[9=\frac{8}{9}=8:9\] and ratio of 24 to \[27=\frac{24}{27}=\frac{24\div 3}{27\div 3}=\frac{8}{9}=8:9\] [dividing numerator and denominator both by 3] Here, 8 : 9 = 24 : 27, so 8 : 9 : : 24 : 27 Hence, given statement is true. (e) We have, 5.2 : 3.9 : : 3 : 4 Ratio of 5.2 to \[3.9=\frac{5.2}{3.9}=\frac{52}{39}\] [multiplying numerator and denominator both by 10] \[=\frac{52\div 13}{39\div 13}=\frac{4}{3}=4:3\] [\[\because \]HCF of 52 and 39 = 13] and ratio of 3 to \[4=\frac{3}{4}=3:4\] Here, \[4:3\ne 3:4\,\text{i}\text{.e}\text{.}\,5.2:3.9\ne 3:4\] Hence, given statement is false. (f) We have, 0.9 : 0.36 : : 10 : 4 \[\therefore \]Ratio of 0.9 to \[0.36=\frac{0.9}{0.36}=\frac{90}{36}\] [multiplying numerator and denominator both by 100] \[=\frac{90\div 18}{36\div 18}=\frac{5}{2}=5:2\] [\[\because \]HCF of 36 and \[90=2\times 3\times 3=18\]] and ratio of 10 to \[4=\frac{10}{4}=\frac{10\div 2}{4\div 2}=\frac{5}{2}=5:2\] [dividing numerator and denominator both by 2] Here, \[0.9:0.36=10:4=5:2,\]so\[0.9:0.36::10:4\] Hence, given statement is true.
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