Question

Find the number, 30% of which is 36.

Answer 1

Hint:Percentage is a ratio of a number to 100, represented by the symbol ‘%’. Percentage of a number is generally represented by the formula \[p\% ofq = r\] , here \[q\] is the number whose percentage is to be found, \[p\] is how much percentage is to be found and \[r\] is the value obtained when \[p\% \] found of \[q\] . In this question we have to find a number whose 30% is given as the value 36. So to find that number we will assume the unknown number as a variable and by using the formula \[p\% ofq = r\] , we will find the
required number.

Complete step by step solution:
Given the percentage 30% of a number is 36
Let the number whose 30% is 36 be \[x\]
Hence we can say 30% of \[x\] is 36

Now we know percentage of number is generally represented as \[p\% ofq = r\] , so by comparing the given data with the formula we can write
 \[
p = 30 \\
q = x \\
r = 36 \\
\]
Hence by substituting the given values in the formula we can write \[30\% of\left( x \right) = 36\]
Then by solving the equation we can write
 \[\dfrac{{30}}{{100}} \times x = 36\]
By further solving this
 \[
x = 36 \times \dfrac{{100}}{{30}} \\
= \dfrac{6}{5} \times 100 \\
= 6 \times 20 \\

= 120 \\
\]
Hence we get \[x = 120\]

Therefore we can say 30% of 120 is equal to36.

Note: Percentage formula is also used to find the share or amount of something in terms of 100. This is generally given by the formula. In this question we can say total value is 120 and the given value is 36 so by substituting the values in the formula we get
 \[
P\% = \dfrac{{36}}{{120}} \times 100 \\
= 30\% \\
\]