Question Number 206399 by BaliramKumar last updated on 13/Apr/24
Commented by mr W last updated on 14/Apr/24
$${since}\:{the}\:{question}\:{asks}\:{the}\:{ratio}\:{of} \\ $$$$“{their}''\:{speeds},\:{answers}\:\left({b}\right),\:\left({c}\right),\:\left({d}\right) \\ $$$${are}\:{all}\:{correct}. \\ $$$${when}\:{the}\:{question}\:{asks}\:{the}\:{ratio}\:{of} \\ $$$${the}\:{speeds}\:{of}\:“{dog},\:{lion}\:{and}\:{fox}'',\: \\ $$$${then}\:{only}\:{answer}\:\left({c}\right)\:{is}\:{correct}. \\ $$
Answered by mr W last updated on 13/Apr/24
$${distance}\:{covered}\:{by}\:{each}\:{jump}\:{from} \\ $$$${dog},\:{lion}\:{and}\:{fox}\:{is}:\:{J}_{{D}} ,\:{J}_{{L}} ,\:{J}_{{F}} \\ $$$${speed}\:{of}\:{dog},\:{lion}\:{and}\:{fox}:\:{v}_{{D}} ,\:{v}_{{L}} ,\:{v}_{{F}} \\ $$$$ \\ $$$$\mathrm{8}{J}_{{D}} =\mathrm{16}{J}_{{L}} =\mathrm{24}{J}_{{F}} \\ $$$$\Rightarrow{J}_{{D}} =\mathrm{2}{J}_{{L}} =\mathrm{3}{J}_{{F}} \\ $$$${t}=\frac{\mathrm{8}{J}_{{D}} }{{v}_{{D}} }=\frac{\mathrm{12}{J}_{{L}} }{{v}_{{L}} }=\frac{\mathrm{15}{J}_{{F}} }{{v}_{{F}} } \\ $$$$\Rightarrow\frac{\mathrm{8}{J}_{{D}} }{{v}_{{D}} }=\frac{\mathrm{6}{J}_{{D}} }{{v}_{{L}} }=\frac{\mathrm{5}{J}_{{D}} }{{v}_{{F}} }\:\Rightarrow\frac{\mathrm{8}}{{v}_{{D}} }=\frac{\mathrm{6}}{{v}_{{L}} }=\frac{\mathrm{5}}{{v}_{{F}} }\: \\ $$$$\Rightarrow{v}_{{D}} :{v}_{{L}} :{v}_{{F}} =\mathrm{8}:\mathrm{6}:\mathrm{5} \\ $$$$\Rightarrow{answer}\:\left({C}\right) \\ $$
Commented by BaliramKumar last updated on 13/Apr/24
$$\mathrm{thanks} \\ $$
Answered by A5T last updated on 13/Apr/24
$${Dog},{lion},{fox}\:{distance}/{jump}={x},{y},{z}\:{resp}. \\ $$$$\Rightarrow\mathrm{8}{x}=\mathrm{16}{y}=\mathrm{24}{z}\Rightarrow{x}=\mathrm{2}{y}=\mathrm{3}{z} \\ $$$${Dog},{lion},{fox}\:{time}/{jump}={t}_{\mathrm{1}} ,{t}_{\mathrm{2}} ,{t}_{\mathrm{3}} \\ $$$$\mathrm{8}{t}_{\mathrm{1}} =\mathrm{12}{t}_{\mathrm{2}} =\mathrm{15}{t}_{\mathrm{3}} \Rightarrow{t}_{\mathrm{1}} =\frac{\mathrm{3}{t}_{\mathrm{2}} }{\mathrm{2}}=\frac{\mathrm{15}{t}_{\mathrm{3}} }{\mathrm{8}} \\ $$$$\frac{{x}}{{t}_{\mathrm{1}} }:\frac{{y}}{{t}_{\mathrm{2}} }:\frac{{z}}{{t}_{\mathrm{3}} }=\frac{{x}}{{t}_{\mathrm{1}} }:\frac{\frac{{x}}{\mathrm{2}}}{\frac{\mathrm{2}{t}_{\mathrm{1}} }{\mathrm{3}}}:\frac{\frac{{z}}{\mathrm{3}}}{\frac{\mathrm{8}{t}_{\mathrm{1}} }{\mathrm{15}}}=\frac{{x}}{{t}_{\mathrm{1}} }:\frac{\mathrm{3}{x}}{\mathrm{4}{t}_{\mathrm{1}} }:\frac{\mathrm{5}{x}}{\mathrm{8}{t}_{\mathrm{1}} }=\mathrm{8}:\mathrm{6}:\mathrm{5} \\ $$
Commented by BaliramKumar last updated on 13/Apr/24
$$\mathrm{thanks} \\ $$