Question

If $16\% $ of $40\% $ of a number is 8, then the number is
A.200
B.225
C.125
D.None of these

Answer 1

Hint: We will assume the number to be x and then we will convert the given percentages into fraction and equate it to 8 using the formula: $x\% {\text{ of y = }}\dfrac{x}{{100}} \times y$ . We will solve the obtained equation to calculate the value of x.

Complete step-by-step answer:
We are given that $16\% $ of $40\% $ of any number is 8.
We need to calculate the value of that number.
Let the number be x.
We will use the formula $x\% {\text{ of y = }}\dfrac{x}{{100}} \times y$ to convert the percentage into fraction.
First of all, we are said that $16\% $ of $40\% $ of a number x i.e. we will first calculate the $40\% $ of x.
Therefore, we can write the percentage as:
$ \Rightarrow 40\% {\text{ of x = }}\dfrac{{40}}{{100}} \times x = \dfrac{{4x}}{{10}}$
Now, $16\% $ of $40\% $ of x can be written as:
$ \Rightarrow 16\% {\text{ of }}40\% {\text{ of x = }}\dfrac{{16}}{{100}} \times \dfrac{{4x}}{{10}}$
In the question, $16\% $ of $40\% $ of x is given as 8. Putting the value and simplifying it further, we get
$
   \Rightarrow 8 = \dfrac{{16}}{{100}} \times \dfrac{{4x}}{{10}} \\
   \Rightarrow 8 = \dfrac{{64x}}{{1000}} \\
   \Rightarrow x = \dfrac{{8 \times 1000}}{{64}} \\
   \Rightarrow x = \dfrac{{8000}}{{64}} = 125 \\
 $
Therefore, the required number, whose $16\% $ of $40\% $ is 8, is calculated to be 125.
Hence, option (C) is correct.

Note: In this question, we have converted the percentages into fraction to solve this question. Percentage, in mathematics, can be defined as a number expressed in the form of a fraction with denominator 100 denoted by the number followed by percentage (%) sign. Or in other words, a percentage is a part of a complete value expressed in hundredths i.e. one percent is one hundredth of a whole.