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Q.1 Determine if the following are in proportion.
(a) 15, 45, 40, 120
(b) 33, 121, 9, 96
(c) 24, 28, 36, 48
(d) 32, 48, 70, 210
(e) 4, 6, 8, 12
(f) 33, 44, 75, 100
Answer :

(a) 15, 45, 40, 120
\(\frac{15}{45} = \frac{1}{3} \)
\(\frac{40}120} = \frac{1}{3} \)
Hence, 15: 45 = 40:120
\(\therefore \)These are in a proportion
(b) 33, 121, 9, 96
\(\frac{33}{121} = \frac{3}{11} \)
\(\frac{9}{96} = \frac{3}{32} \)
Hence 33:121 \(\neq \)9: 96
\(\therefore \)These are not in a proportion
(c) 24, 28, 36, 48
\(\frac{24}{28} = \frac{6}{7} \)
\(\frac{36}{48} = \frac{3}{4} \)
Hence, 24: 28 \(\neq \)36:48
\(\therefore \) These are not in a proportion
(d) 32, 48, 70, 210
\(\frac{32}{48} = \frac{2}{3} \)
\(\frac{70}{210} = \frac{1}{3} \)
Hence, 32: 48 \(\neq \)70: 210
\(\therefore \)These are not in a proportion
(e) 4, 6, 8, 12
\(\frac{4}{6} = \frac{2}{3} \)
\(\frac{8}{12} = \frac{2}{3} \)
Hence 4: 6 = 8: 12
\(\therefore \) These are in a proportion
(f) 33, 44, 75, 100
\(\frac{33}{44} = \frac{3}{4} \)
\(\frac{75}{100} = \frac{3}{4} \)
Hence, 33:44 = 75: 100
\(\therefore \)These are in a proportion