Question

If $A:B=5:6$ and $B:C=4:7$, Find $A:B:C$.

Answer 1

Solve for the required ratio

Given that $A:B=5:6$ and $B:C=4:7$

$\begin{array}{clcl}\Rightarrow & A:B& =& 5:6\\ & B:C& =& 4:7\\ \Rightarrow & \left(A:B\right)\times 2& =& \left(5:6\right)\times 2\\ & \left(B:C\right)\times 3& =& \left(4:7\right)\times 3\\ \Rightarrow & A:B& =& 10:\boxed{12}\\ & B:C& =& \boxed{12}:21\\ \Rightarrow & A:B:C& =& 10:12:21\end{array}$

Hence the required ratio of $A:B:C$ is $10:12:21$