Question

The $160\% $ of what number is \[32\]?

Answer 1

Hint: In the given question, we are required to calculate a specific number whose $160\% $corresponds to the number provided to us in the problem, \[32\]. We must remember the formula for finding a specific percentage of a number as: $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $. Percentage of a number corresponds to the share or share in the whole thing.

Complete step by step answer:
So, we find the number whose $160\% $ corresponds to the number \[32\] by using the formula for percentage as $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $. Let us assume $160\% $ of the number x to be equal to \[32\].So, the whole corresponds to the number x and the part corresponds to the number \[32\] in this case. Also, the percentage is given to us as $160\% $. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow 160\% = \dfrac{{32}}{x} \times 100\% $

Now, we have to find the value of $x$ in the above equation. We use the method of transposition to shift the terms in the equation and find the value of the variable. Shifting the variable to left side of equation and constants to the right side of the equation, we get,
$ \Rightarrow x = \dfrac{{32}}{{160\% }} \times 100\% $
Simplifying the calculations, we get,
$ \Rightarrow x = \dfrac{{32}}{{16}} \times 10$
Simplifying the calculations by cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x = \dfrac{2}{1} \times 10$
$ \Rightarrow x = 20$
So, the value of x is $20$.

Hence, $160\% $of the number $20$ is equal to \[32\].

Note: The percentage formula $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $ can be used to find any parameter in the equation given the other parameters. The final answer must be given in the whole number quantity by cancelling the common factors in numerator and denominator. Abbreviation for percentage is ‘pct’ or ‘pc’.