Question

Let us pick two random integers, say $ x $ and $ y $ . It has given that $ 10\% $ of $ x $ is $ y $ . Then what will be $ y\% $ of $ 80 $ be:
A. $ 8\% $ of $ x $
B. $ 8\% $ of $ y $
C. $ 4\% $ of $ x $
D. $ 4\% $ of $ y $

Answer 1

Hint: Use the basics of the percentage that $ a\% $ of a value $ b $ is given by $ \dfrac{{ab}}{{100}} $ . Calculate the $ y\% $ of $ 80 $ and then use the relationship given between $ x $ and $ y $ to get the answer in the form of percentage of some integers $ x $ or $ y $ .

Complete step-by-step answer:
Use the basics of the percentage that $ a\% $ of a value $ b $ is given by $ \dfrac{{ab}}{{100}} $ . Use this rule to solve the percentage given in the question and find the relation between two.
It is given that $ 10\% $ of $ x $ is $ y $ . This gives the relationship between the integers $ x $ and $ y $ that is $ \dfrac{x}{{10}} = y $ .
Now calculate the $ y\% $ of $ 80 $ :
 $
  y\% \;{\text{of}}\;80 = \dfrac{y}{{100}} \times 80 \\
   = \dfrac{{8y}}{{10}} \;
  $
Now use the relationship between both the integers $ \dfrac{x}{{10}} = y $ .
 $
  y\% \;{\text{of}}\;80 = \dfrac{{8y}}{{10}} \\
   = \dfrac{8}{{10}} \times \dfrac{x}{{10}} \\
   = \dfrac{8}{{100}} \times x \\
   = 8\% \;{\text{of}}\;x \;
  $
Hence, the value $ y\% $ of $ 80 $ is equal to the value $ 8\% $ of $ x $ .
So, the correct answer is “Option A”.

Note: The value of $ a\% $ of a value $ b $ is given by $ \dfrac{{ab}}{{100}} $ .Take a note that the condition given is $ 10\% $ of $ x $ is $ y $ which means $ \dfrac{x}{{10}} = y $ not $ 10x = y $ which makes most of the confusion. At last make the value in the form of the percentage of the integer.