Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}\frac{1}{a}:\frac{1}{b}:\frac{1}{c}=3:4:5,\mathrm{then}a:b:c= \\ \left(\mathrm{a}\right)5:4:3\left(\mathrm{b}\right)20:15:12\left(\mathrm{c}\right)9:12:15\left(\mathrm{d}\right)12:15:20 \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},\frac{1}{a}:\frac{1}{b}:\frac{1}{c}=3:4:5 \\ \Rightarrow \frac{1}{a}:\frac{1}{b}=3:4\mathrm{and}\frac{1}{b}:\frac{1}{c}=4:5 \\ \Rightarrow \frac{1}{a}÷\frac{1}{b}=\frac{3}{4}\mathrm{and}\frac{1}{b}÷\frac{1}{c}=\frac{4}{5} \\ \Rightarrow \frac{1}{a}\times \frac{b}{1}=\frac{3}{4}\mathrm{and}\frac{1}{b}\times \frac{c}{1}=\frac{4}{5} \\ \Rightarrow \frac{b}{a}=\frac{3}{4}\mathrm{and}\frac{c}{b}=\frac{4}{5} \\ \Rightarrow \frac{a}{b}=\frac{4}{3}\mathrm{and}\frac{b}{c}=\frac{5}{4}\left(\mathrm{Reciprocal}\mathrm{of}\mathrm{both}\mathrm{sides}\right) \\ \Rightarrow \frac{a}{b}=\frac{4\times 5}{3\times 5}\mathrm{and}\frac{b}{c}=\frac{5\times 3}{4\times 3} \\ \Rightarrow \frac{a}{b}=\frac{20}{15}\mathrm{and}\frac{b}{c}=\frac{15}{12} \\ \Rightarrow a:b=20:15\mathrm{and}b:c=15:12 \\ \therefore a:b:c=20:15:12 \end{gathered}$$

Hence, the correct alternative is option (b).