Question

4. (i) If $A:B=2:3,B:C=4:5\mathrm{and}C:D=6:7$, find $A:D$.

Answer 1

Calculation of the ratio $A:D$:

The given ratios are equivalent to $\frac{A}{B}=\frac{2}{3}$, $\frac{B}{C}=\frac{4}{5}$ and $\frac{C}{D}=\frac{6}{7}$.

Now,

$$\begin{gathered} A:D=\frac{A}{D} \\ \Rightarrow A:D=\frac{A}{B}\times \frac{B}{C}\times \frac{C}{D}(MultiplyinganddividingbyBandC) \\ \Rightarrow A:D=\frac{2}{3}\times \frac{4}{5}\times \frac{6}{7}(Substitutingthevalues) \\ \therefore A:D=\frac{16}{35} \end{gathered}$$

Final Answer: The ratio is $16:35$.