Question

If x is $ 5 $ percent of r and r is $ 20 $ percent of s, what percent of s is x?
A. $ 1\% $
B. $ 4\% $
C. $ 10\% $
D. $ 40\% $
E. $ 100\% $

Answer 1

Hint: Here we will convert the given word statements in to the form of mathematical expressions. As we are given two statements, find the correlation between the two and find the required value.

Complete step-by-step answer:
Given that “x” is percent of r
Convert it in the form of mathematical expressions and convert the given percentage in the form of fraction.
It can be re-written as-
 $ x = \dfrac{5}{{100}} \times r\; $ .... (A)
Also, given that the r is $ 20 $ percent of s
Convert it in the form of mathematical expressions and convert the given percentage in the form of fraction.
It can be re-written as-
 $ r = \dfrac{{20}}{{100}} \times s\; $ .... (B)
Now, substitute the values of the equation (B) in the equation (A)
 $ x = \dfrac{5}{{100}} \times \dfrac{{20}}{{100}} \times s\;\; $
Simplify the above equation –
 $ x = \dfrac{1}{{100}} \times \dfrac{{100}}{{100}} \times s\;\; $
Common multiples from the numerator and denominator cancel each other. Therefore remove from the numerator and the denominator.
 $ \Rightarrow x = \dfrac{1}{{100}} \times s\;\; $
Convert the above fraction in the form percentage-
 $ \Rightarrow x = 1\% \times s\;\; $
So, the correct answer is “Option A”.

Note: Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from a certain size whereas percentage is the number or ratio expressed as a fraction of a hundred. Know the difference between the fraction and the percentage and apply accordingly.
Percentages are widely used in many different areas such as discounts in shops, bank interests and many other Medias.