Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{a}{2}=\frac{b}{3}=\frac{c}{4},\mathrm{then}a:b:c= \\ \left(\mathrm{a}\right)2:3:4\left(\mathrm{b}\right)4:3:2\left(\mathrm{c}\right)3:2:4\left(\mathrm{d}\right)\mathrm{None}\mathrm{of}\mathrm{these} \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},\frac{a}{2}=\frac{b}{3}=\frac{c}{4} \\ \Rightarrow \frac{a}{2}=\frac{b}{3}\mathrm{and}\frac{b}{3}=\frac{c}{4} \\ \Rightarrow 3a=2b\mathrm{and}4b=3c\left(\mathrm{By}\mathrm{cross}\mathrm{multiplication}\right) \\ \Rightarrow \frac{a}{b}=\frac{2}{3}\mathrm{and}\frac{b}{c}=\frac{3}{4} \\ \Rightarrow a:b=2:3\mathrm{and}b:c=3:4 \\ \therefore a:b:c=2:3:4 \end{gathered}$$

Hence, the correct alternative is option (a).