Question

If $33\dfrac{1}{3}\% \,of\,A = 1.5\,of\,B = \dfrac{1}{8}\,of\,C$, then $A:B:C$ is
A.$24 :2:9$
B.$2:9:24$
C.$9:2:24$
D.$9:24:2$

Answer 1

Hint: Convert all the values into fractions and find the ratios of $A:B$,$B:C$ and $C:A$, With the help of one ratio value try to compensate the other ratio of same value, do the same with the other ratios and we will be able to find the ratio of A:B:C

Complete step-by-step answer:
Given that $33\dfrac{1}{3}\% \,of\,A = 1.5\,of\,B = \dfrac{1}{8}\,of\,C$,
So,
$
   \Rightarrow 33\dfrac{1}{3}\% \left( A \right) = \dfrac{{100}}{3}\% \left( A \right) = \dfrac{{100}}{3} \times \dfrac{1}{{100}}\left( A \right) = \dfrac{A}{3}........\left( 1 \right) \\
   \Rightarrow 1.5\left( B \right) = \dfrac{{3B}}{2}........\left( 2 \right) \\
   \Rightarrow \dfrac{1}{8}\left( C \right) = \dfrac{C}{8}..........\left( 3 \right) \\
 $
Now with the help of (1) and (2)
$
   \Rightarrow \dfrac{A}{3} = \dfrac{{3B}}{2} \\
   \Rightarrow \dfrac{A}{B} = \dfrac{9}{2}........\left( 4 \right) \\
 $
Now with the help of (2) and (3)
$
   \Rightarrow \dfrac{{3B}}{2} = \dfrac{C}{8} \\
   \Rightarrow \dfrac{B}{C} = \dfrac{1}{{12}}........\left( 5 \right) \\
$
Now with the help of (3) and (1)
$
   \Rightarrow \dfrac{C}{8} = \dfrac{A}{3} \\
   \Rightarrow \dfrac{A}{C} = \dfrac{3}{8}........\left( 6 \right) \\
 $
Now with the help of (4) try to compensate the same value of A in (6)
We have, $\dfrac{A}{B} = \dfrac{9}{2}$and $\dfrac{A}{C} = \dfrac{3}{8}$, try to make the value of A same
$
   \Rightarrow \dfrac{A}{C} = \dfrac{3}{8} \\
   \Rightarrow d\dfrac{A}{C} = \dfrac{3}{8} \times \dfrac{3}{3} \\
   \Rightarrow \dfrac{A}{C} = \dfrac{9}{{24}}.......\left( 7 \right) \\
 $
Now we have $A = 9$
Now with the help of (7) try to compensate the same value of C and B in (5)
We have, $\dfrac{A}{C} = \dfrac{9}{{24}}$and $\dfrac{B}{C} = \dfrac{1}{{12}}$, try to make the value of C same
\[
   \Rightarrow \dfrac{B}{C} = \dfrac{1}{{12}} \\
   \Rightarrow \dfrac{B}{C} = \dfrac{1}{{12}} \times \dfrac{2}{2} \\
   \Rightarrow \dfrac{B}{C} = \dfrac{2}{{24}}.........\left( 8 \right) \\
\]
From (7) and (8), we have the ratio of $A:B:C$ as $9:2:24$.
So option C is correct.

Note: Always in ratios and proportions try to compensate for the values of the same variable with the help of others, There is no other alternative other than short cut.