Question

x% of y is y% of:
(a)x
(b)$\dfrac{y}{100}$
(c)$\dfrac{x}{100}$
(d)100x

Answer 1

Hint: Start by considering that x% of y is equal to y% of k. Then write the mathematical interpretation of the phrases “x% of y” and “y% of k” separately. Equate both the expressions to get the value of k.

Complete step-by-step answer:

Before starting with the solution, let us discuss percentage and its importance. A percentage is actually a quantity that is used to get the relation between the whole and a part of a specific thing. A percentage, in other words, is the amount or a number in each hundred. Now let us try to understand the importance of percentage from a day to day example. Suppose two students appeared for an exam with maximum marks of 300, and he scored 250, whereas others appeared an exam with maximum marks 200 and scored 200 in it. Now if you see the first student has scored more marks but actually the percentage of the second student is higher and hence we can say that the second student is better than the first one.

To start with the solution, let us first try to interpret the phrase “x% of y “ in mathematical terms. So, this can be written in form of mathematical expression as:

$x \%\text{ of y = }\dfrac{x}{100}\times y=\dfrac{xy}{100}$

Now we let y% of k to be equal to x% of y. So, we get

$x \%\text{ of y = y }\!\!%\!\!\text{ of k}$

$\Rightarrow \dfrac{xy}{100}\text{ = }\dfrac{yk}{100}$

$\Rightarrow k=x$

Therefore, the answer to the above question is option (a).

Note: Mathematically x% of y and y% of x are equal but don’t form the misconception that they are the same. Actually they have different interpretations when we use them in questions.