• # question_answer 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

 (a) We have, $15:45=\frac{15}{45}=\frac{1}{3}$ and                   $40:120=\frac{40}{120}=\frac{1}{3}$ Since,                $15:45=40:120$ So, 15, 45, 40, 120 are in proportion. Other method: We have, Product of extremes $=15\times 120=1800$ Product of middle terms $=45\times 40=1800$ Product of extremes = Product of middle terms Hence, 15, 45, 40, 120 are in proportion. (b) We have $33:121=\frac{33}{121}=\frac{3}{11}$ and                      $9:96=\frac{9}{96}=\frac{3}{32}$ Therefore,   $\frac{3}{11}\ne \frac{3}{32}$ So,            $~33:121\ne 9:96$ Thus, 33, 121, 9, 96 are not in proportion. Other method: We have, Product of extremes $=33\times 96=3168$ Product of middle terms $=121\times 9=1089$ Product of extremes $\ne$ Product of middle terms Hence, 33, 121, 9, 96 are not in proportion. (c) We have, $~24:28=\frac{24}{28}=\frac{6}{7}$ and                    $36:48=\frac{36}{48}=\frac{3}{4}$ Since,                $\frac{6}{7}\ne \frac{3}{4}$ Therefore,   $24:28\ne 36:48$ They, 24, 28, 36, 48 are not in proportion. (d) We have,     $32:48=\frac{32}{48}=\frac{2}{3}$ and                      $70:210=\frac{70}{210}\text{=}\frac{1}{3}\text{ }$ Since,                $\frac{2}{3}\ne \frac{1}{3}$ Therefore,   $32:48\ne 70:210$ Hence, 32, 48, 70, 210 are not in proportion. (e) We have,      $4:6=\frac{4}{6}=\frac{2}{3}$ and                   $8:12=\frac{8}{12}=\frac{2}{3}$ So,                   $4:6=8:12$ Therefore, 4, 6, 8, 12 are in proportion. Other method : We have Product of extremes $=4\times 12=48$ Product of middle terms $=6\times 8=48$ Product of extremes = product of middle terms Hence, 4, 6, 8, 12 are in proportion. (f) We have,      $33:44=\frac{33}{44}=\frac{3}{4}$ and                   $75:100=\frac{75}{100}=\frac{3}{4}$ So,                   $33:44=75:100$ Therefore, 33, 44, 75, 100 are in proportion.