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What number is $78\% $ of $50$?
A. $32$
B. $35$
C. $36$
D. $39$
E. $41$

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Last updated date: 19th Jul 2024
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Answer
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Hint: In the given question, we are required to calculate a specific percentage of the number when the whole quantity is provided. We must remember the formula for finding a specific percentage of a number as: $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $. So, we will substitute the known quantities in the formula. Percentage of a number corresponds to the share or share in the whole thing.

Complete step by step answer:
In this specific question, we are required to find $78\% $ of the number given to us, $50$.
So, we find the number that corresponds to $78\% $ of $50$ by using the formula for percentage as $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $.

Let us assume $78\% $ of $50$ to be equal to $x$. So, the whole corresponds to the number $50$ and the part corresponds to the number $x$ in this case. Also, the percentage is given to us as $78\% $. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow 78\% = \dfrac{x}{{50}} \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. Keeping the variable on right side of equation and constants to the left side of the equation, we get,
$ \Rightarrow 78\% \times \dfrac{{50}}{{100\% }} = x$
Simplifying the calculations, we get,
$ \Rightarrow x = 78 \times \dfrac{{50}}{{100}}$
Simplifying the calculations by cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x = \dfrac{{78}}{2}$
$ \therefore x = 39$
So, the value of x is $39$.
Hence, $39$ is $78\% $ of $50$.

Therefore, option (D) is the correct answer.

Note: Percentage is defined as the relative value that indicates hundredth parts of any quantity or it can be defined as a number or ratio represented in the form of fractions of $100$ and is represented by the sign $\% $. The abbreviations used to represent the percentage are “pct” or ”pc”. 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. If the partial number is greater than the whole quantity, the corresponding percentage will be greater than $100\% $ as $100\% $ is represented by the whole quantity.