Question

The $ 66\dfrac{2}{3}\% $ of what number is $ 12 $ ?

Answer 1

Hint: The percent is defined by how many things are present or there per $ 100 $ things hence the word cent meaning hundred. So if something is $ 10\% $ it will mean that out of total $ 100 $ things only $ 10 $ things are present. Also say if a number is half of something that will mean it is $ 50\% $ of something. The question asks us to tell what number will be $ 100 $ if $ 66\dfrac{2}{3} $ is $ 12 $ . First we will have to find how much is $ 66\dfrac{2}{3} $ of $ 100 $ in terms of fraction, then we will reverse that fraction to get the value of the original number whose $ 66\dfrac{2}{3}\% $ is $ 12 $ .

Complete step by step solution:
First we will find $ 66\dfrac{2}{3} $ will be what fraction of $ 100 $ , we will then reverse the fraction to get the value of the required number.
Now we will divide the number $ 66\dfrac{2}{3} $ by $ 100 $ , to get the fraction,
 $ \Rightarrow \dfrac{{66\dfrac{2}{3}}}{{100}} $
 $ \Rightarrow \dfrac{{200}}{{300}} $ ,
 $ \Rightarrow \dfrac{2}{3} $
Now we will reverse this fraction and multiply by the number $ 12 $ , to get the final answer,
The ratio on reversing gives,
 $ \dfrac{3}{2} $ ,
We will now multiply the above ratio with the number $ 12 $ ,
\[\dfrac{3}{2} \times 12\]
We get $ 18 $ .
Thus $ 66\dfrac{2}{3}\% $ of the number $ 18 $ is $ 12 $ .
So, the correct answer is “ $ 18 $ ”.

Note: We can also check this answer by multiplying the number $ 18 $ with the initial ratio to see if it results in $ 12 $ , the calculation will go as follows,
 $ 18 \times \dfrac{2}{3} $
Which upon solving will yield us with $ 12 $ .
Also important to note is to remember the ratio to percent conversion of very common percent to aid rapid calculation in the examination, The common percent to ratio conversions are given below,
 $
  33\dfrac{1}{3}\% \to \dfrac{1}{3} \\
  66\dfrac{2}{3}\% \to \dfrac{2}{3} \\
  50\% \to \dfrac{1}{2} \;
 $