Question

If $A:B=3:4,B:C=5:7,$ find $A:B:C$

Answer 1

$A:B=3:4$

Let $k$ be the common factor between $A$ and $B$.

so, $A$ $=3k$ and $B$ $=4k$.

and, $B:C=5:7$

Let $x$ be the common factor between $B$ and $C$.

so, $B$ $=5x$ and $C$ $=7x$

$\therefore 4k=5x\left[\text{Both are values of B}\right]$

$x=\frac{4k}{5}$

$A:B:C=3k:4k:7x$

$=3k:4k:7\left(\frac{4k}{5}\right)$

$=15k:20k:\frac{28k}{5}$

$=15:20:28\left[\text{on multiplying}\frac{5}{k}\text{to each}\right]$

Hence $A:B:C=15:20:28$