Question

Find the value of $9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240$
A.15.8
B.23.7
C.28.5
D.None of these

Answer 1

Hint: Percentage of a number can be calculated by multiplying the given percentage by the number and dividing by 100, or we can say $x\% $ of \[y = \dfrac{x}{{100}} \times y\]. We will calculate the value of each part individually and then substitute the respective values in the expression to get the final answer.

Complete step by step solution:

We know that $x\% $ of a number$y$can be calculated by as following:
$x\% $ of \[y = \dfrac{x}{{100}} \times y\]
Thus, $x\% $ of \[y = \dfrac{{xy}}{{100}}\]
Now, in order to find the value of $9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240$, we will calculate individual terms and then operate the expression.
Firstly, we will calculate $9.3\% $ of $500$
$9.3\% $ of $500 = \dfrac{{9.3}}{{100}} \times 500$
$9.3\% $ of $500 = 9.3 \times 5$
$9.3\% $ of $500 = 46.5$
Therefore, $9.3\% $ of $500$ is $46.5$
Now, we will calculate $4.8\% $ of $250$
$4.8\% $ of $250 = \dfrac{{4.8}}{{100}} \times 250$
$4.8\% $ of $250 = \dfrac{{4.8}}{2} \times 5$
$4.8\% $ of $250 = 2.4 \times 5$
$4.8\% $ of $250 = 12$
Therefore, $4.8\% $ of $250$ is $12$
Now, we will calculate $2.5\% $ of $240$
$2.5\% $ of $240 = \dfrac{{2.5}}{{100}} \times 240$
$2.5\% $ of $240 = \dfrac{{2.5}}{5} \times 12$
$2.5\% $ of $240 = 0.5 \times 12$
$2.5\% $ of $240 = 6$
Therefore, $2.5\% $ of $240$ is $6$
Now, we will calculate the value of given expression $9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240$
Substituting,
$9.3\% $ of $500 = 46.5$
$4.8\% $ of $250 = 12$
$2.5\% $ of $240 = 6$
Thus, $9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240 = 46.5 - 12 - 6$
$9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240 = 46.5 - 18$
$9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240 = 28.5$
Hence, the value of expression $9.3\% $ of $500 - 4.8\% $of $250 - 2.5\% $of $240$is $28.5$
Therefore, option c $28.5$is correct
Note: While calculating the percentages of numbers, one must prevent calculation errors and calculate the value carefully. Moreover, while finding the value of expression, signs must be taken care of.
In problems related to a percentage, the student must take care of the following and not get confused in problems related to calculating the percentage of a number and calculating what percentage a number is of another number:
When it’s required to find, x% of y,
$x\% $ of \[y = \dfrac{x}{{100}} \times y\]
And, when it’s required to find, what percentage is x of y,
$\dfrac{x}{y} \times 100$
Gives the required percentage. So, it’s necessary to remember these two procedures separately.