If $A : B = 3 : 4$ and $B : C = 5 : 6$, what percent of $C$ is $A$?

If $A : B = 3 : 4$ and $B : C = 5 : 6$, what percent of $C$ is $A$?
  1. $50\%$
  2. $62.5\%$
  3. $66\dfrac{2}{3}\%$
  4. $75\%$

Solution

Combine ratios: $A:B:C = (3 \cdot 5) : (4 \cdot 5) : (4 \cdot 6) = 15 : 20 : 24$. So $\dfrac{A}{C} = \dfrac{15}{24} = \dfrac{5}{8} = 0.625 = 62.5\%$.

Asked in: IMO

Practice more COMPARING QUANTITIES questions on Aicharya