Question

What is \[120\% \] of \[50\]?

Answer 1

Hint: Here, we have to calculate a specific percentage of a number when the whole quantity is provided i.e., \[120\% \] of \[50\]. Percentage of a number corresponds to the share in the whole thing. We will use the formula for finding a specific percentage of a number that is given by \[Percentage = \dfrac{{Part}}{{Whole}} \times 100\% \].

Complete step by step answer:
In this question, we are required to find \[120\% \] of the given number \[50\].
We will use the formula for the percentage i.e., \[Percentage = \dfrac{{Part}}{{Whole}} \times 100\% \] to find the number that corresponds to \[120\% \] of \[50\].
Let us assume that \[120\% \] of \[50\] is equal to \[x\].
So here the whole corresponds to the number \[50\] and the part corresponds to the number \[x\]. Also, the percentage is given as \[120\% \].
Substituting the known values given in the question in the above mentioned formula, we get
\[ \Rightarrow 120\% = \dfrac{x}{{50}} \times 100\% \]
To find the value of \[x\], we will use the method of transposition to shift the terms in the equation. Keeping the variable on the right side of the equation and constants to the left side of the equation, we get
\[ \Rightarrow x = \dfrac{{120\% \times 50}}{{100\% }}\]
On simplification, we get
\[ \Rightarrow x = \dfrac{{120 \times 50}}{{100}}\]
On cancelling the common factors from the numerator and the denominator, we get
\[ \Rightarrow x = 12 \times 5\]
On multiplication, we get
\[ \Rightarrow x = 60\]
Here, we can see that the answer we get i.e., \[60\] is more than the given number \[50\]. This is because the percentage asked here is more than \[100\% \].
Therefore, \[120\% \] of \[50\] is \[60\].

Note:
A percentage is often denoted using the percent sign i.e., \['\% '\] and is a dimensionless number. Percentage has no unit of measurement. It can be expressed as decimal or fraction. Also note that we can express any given percentage as a fraction by just dividing it by \[100\]. If we have to calculate the percentage then both quantities should have the same unit. In these problems the word “of” denotes multiplication.