Question

If 0.06% of a number is 84, then 30% of that number is
A. \[25.2\]
B. \[420\]
C. \[42000\]
D. \[2520\]

Answer 1

Hint:
Here we use the concept of percentage which means the part of a complete value. Percentage is always denoted by the sign % and opens up by dividing the value by \[100\]. Say we can write \[23\% \]of a value as \[\dfrac{{23}}{{100}}\] and multiply it to the value of which we are calculating the percentage.
* When any number is \[x\% \] of another number, then the first number is \[\dfrac{x}{{100}}\]times of the other number i.e. \[m\% \] of \[x\] \[ = (\dfrac{m}{{100}}) \times x\] i.e. \[{(\dfrac{m}{{100}})^{th}}\] part of \[x\]
* Also here we use the unitary method to calculate the initial number and then finding out the required percentage of the number.
* In unitary method we calculate the value of a single unit by dividing the total value by the number of units, and to find the value of multiple units we multiply the value of a single unit to the number of units.

Complete step by step solution:
Let the number be \[x\].
Given, 0.06% of a number is 84
0.06% of the number \[x\] is \[\dfrac{{0.06}}{{100}}x\]
And \[\dfrac{{0.06}}{{100}}x\] is given as 84.
Equate \[\dfrac{{0.06}}{{100}}x\] to 84, that is \[\dfrac{{0.06}}{{100}}x = 84\]
Divide both sides of the equation by 0.06 and simplify.
\[
  \dfrac{{\dfrac{{0.06}}{{100}}x}}{{0.06}} = \dfrac{{84}}{{0.06}} \\
  \dfrac{x}{{100}} = 1400 \\
 \]
Multiply both sides of the equation by 100 to obtain the value of \[x\].
\[x = 140000\]
30% of the number implies \[\dfrac{{30}}{{100}}\]times the value of\[x\].
Multiply \[\dfrac{{30}}{{100}}\] to the obtained value of \[x\] to obtain the answer.
\[\dfrac{{30}}{{100}}\left( {140000} \right) = 42000\]

Therefore, Option C is correct.

Note:
 In these types of questions, students should evaluate using the unitary method carefully, as this question involves decimal values and these values open up. Also percentage of any value is always less than or equal to the value because percentage is a part of the value so it can never be greater than the value.