Question

What percent of $270\,kg$ is $108\,kg$?

Answer 1

Hint: In the given question, we are required to calculate the percentage of a given weight that corresponds to another quantity of weight. 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 and find the value of the unknown by the means of the transposition method.

Complete step by step answer:
In this specific question, we are required to find the percentage that represents the weight $108\,kg$ out of $270\,kg$.Let us assume the required percentage to be $x$ percent. So, we have to find the value of $x$ to get to the required answer.

We will use the formula for finding the percentage of a number in the problem as,
$\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $
So, the whole corresponds to the quantity $270\,kg$ and the part corresponds to the weight $108\,kg$ in this case. Also, the percentage is assumed to be x. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow x\% = \dfrac{{108\,kg}}{{270\,kg}} \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. Simplifying the calculations and cancelling common factors in numerator and denominator, we get,
$ \Rightarrow x\% = 4 \times 10\% $
Carrying out the multiplication, we get,
$ \Rightarrow x\% = 40\% $
So, the value of $x$ is $40$.

Hence, $108\,kg$ is $40$ percent of $270\,kg$.

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.