Question

If $7A=5B=2C$ find $A:B:C$

1.) $35:14:10$

2.) $14:10:35$

3.) $2:5:7$

4.) $10:14:35$

Answer 1

Given $7A=5B=2C$
$\Rightarrow 7A=5B$ and $5B=2C$
$\Rightarrow \frac{A}{B}=\frac{5}{7}$ .......(i) and $\frac{B}{C}=\frac{2}{5}$........(ii)
To find $A:B:C$: We shall make "$B$" corresponding values equal in above two fractions.
So, multiply equation(i) by $\frac{2}{2}$ and equation(ii) by $\frac{7}{7}$,
we get, $\frac{A}{B}=\frac{5}{7}\times \frac{2}{2}$ and $\frac{B}{C}=\frac{2}{5}\times \frac{7}{7}$
$\frac{A}{B}=\frac{10}{14}$ and $\frac{B}{C}=\frac{14}{35}$

Therefore, $A:B=10:14$ and $B:C=14:35$
Hence, $A:B:C=10:14:35$
Thus, the correct option is $\left(4\right)$ ($10:14:35$)