Question Number 122705 by john santu last updated on 19/Nov/20
Commented by liberty last updated on 19/Nov/20
$$\Rightarrow{a}\::\:{b}\:=\:\mathrm{2}\::\:\mathrm{3}\: \\ $$$$\Rightarrow{b}\::\:{c}\:=\:\mathrm{3}\::\:\mathrm{4} \\ $$$$\Rightarrow\:{c}\::\:{d}\:=\:\mathrm{5}\::\:\mathrm{6}\: \\ $$$${then}\:{a}\::\:{b}\::\:{c}\::\:{d}\:=\:\mathrm{10}\::\:\mathrm{15}\::\:\mathrm{20}\::\:\mathrm{24} \\ $$$${we}\:{get}\:{a}+{b}+{c}+{d}\:=\:\mathrm{69}{k}\:=\:\mathrm{21}.\mathrm{2} \\ $$$${k}\:=\:\frac{\mathrm{21}.\mathrm{2}}{\mathrm{69}}\:=\:\frac{\mathrm{106}}{\mathrm{345}} \\ $$$$\begin{cases}{{a}=\mathrm{10}{k}\:,\:{b}\:=\:\mathrm{15}{k}}\\{{c}=\mathrm{20}{k}\:,\:{d}=\mathrm{24}{k}}\end{cases} \\ $$