Answer:
(a) We have, 15, 45, 40, 120 \[\therefore \]Ratio of 15 to 45 \[=\frac{15}{45}=\frac{15\div 15}{45\div 15}\] [\[\because \]HCF of 15 and 45 = 15] \[=\frac{1}{3}=1:3\] and ratio of 40 to 120 \[=\frac{40}{120}=\frac{40\div 40}{120\div 40}=\frac{1}{3}=1:3\] [\[\because \]HCF of 40 and \[120=\frac{1}{3}=1:3\]] Here, 15 : 45 = 40 : 120 = 1 : 3 Therefore, 15, 45, 40, and 120 are in proportion. (b) We have, 33, 121, 9, 96 \[\therefore \] Ratio of 33 to \[121=\frac{33}{121}=\frac{33\div 11}{121\div 11}\] [\[\because \] HCF of 33 and 121 = 11] and ratio of 9 to 96 \[=\frac{9}{96}=\frac{9\div 3}{96\div 3}\] [\[\because \]HCF of 9 and 96 = 3] \[=\frac{3}{32}=3:32\] Here,\[3:11\ne 3:32\] i.e. \[33:121\ne 9:96\] Therefore, 33, 121, 9 and 96 are not in proportion. (c) We have, 24, 28, 36, 48 \[\therefore \] Ratio of 24 to 28 \[=\frac{24}{28}=\frac{24\div 4}{28\div 4}\] [\[\because \]HCF of 24 and\[28=2\times 2=4\]] \[=\frac{6}{7}=6:7\] and ratio of 36 to 48 \[=\frac{39}{48}=\frac{36\div 12}{48\div 12}=\frac{3}{4}=3:4\] [\[\because \]HCF of 36 and \[48=2\times 2\times 3=12\]] Here,\[6:7\ne 3:4\] i.e.\[24:28\ne 36:48\] Therefore, 24, 28, 36 and 48 are not in proportion. (d) We have, 32, 48, 70, 210 \[\therefore \]Ratio of 32 to \[48=\frac{32}{48}=\frac{32\div 16}{48\div 16}=\frac{2}{3}=2:3\] [\[\therefore \]HCF of 32 and \[48=2\times 2\times 2\times 2=16\]] and ratio of 70 to \[210=\frac{70}{210}=\frac{70\div 70}{210\div 70}=\frac{1}{3}=1:3\] [\[\because \]HCF of 70 and\[210=2\times 5\times 7=70\]] Here, \[2:3\ne 1:3\]i.e.\[32:48\ne 70:210\] Therefore, 32, 48, 70 and 210 are not in proportion. (e) We have; 4, 6, 8, 12 \[\therefore \] Ratio of 4 to \[6=\frac{4}{6}=\frac{4\div 2}{6\div 2}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 2] and ratio of 8 to\[12=\frac{8}{6}=\frac{8\div 4}{12\div 4}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 4] Here, 4 : 6 = 8 : 12 = 2 : 3 Therefore, 4, 6, 8 and 12 are in proportion. (f) We have 33, 44, 75, 100 \[\therefore \] Ratio of 33 to \[44=\frac{33}{44}=\frac{33\div 11}{44\div 11}\] [\[\because \]HCF of 33 and 44 = 11] \[=\frac{3}{4}=3:4\] and ratio of 75 to \[100=\frac{75}{100}=\frac{75\div 25}{100\div 25}=\frac{3}{4}=3:4\] [\[\because \]HCF of 75 and\[100=5\times 5=25\]] Here, 33 : 44 = 75 : 100 = 3 : 4 Therefore, 33, 44, 75 and 100 are in proportion.
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