Question

The salary of Meenal is $50\% $ more than that of Ayushi. By what percent is Ayushi’s salary less than that of Meenal’s?

Answer 1

Hint: In the given question, we first assume the salary of one of the two persons as a variable. Then, we calculate the salary of another person using the given percentage relation. Then, we find the difference between the salaries of both people and find the required percentage using the formula: $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $. Percentage of a number corresponds to the share or share in the whole thing.

Complete step by step solution:
First, let us assume Ayushi’s salary is $x$ rupees.
Then, we know that Meenal’s salary is $50\% $ more than this. This means Meenal’s salary will be $x+ 50\% \text{ of } x$
So, we find the number that corresponds to $50\% $ of x by using the formula for percentage as $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $.
Let us assume $50\% $ of $x$ to be equal to $y$.
So, the whole corresponds to the number $x$ and the part corresponds to the number y in this case. Also, the percentage is given to us as $50\% $. So, we substitute these known values in the above mentioned formula. So, we get,
$ \Rightarrow 50\% = \dfrac{y}{x} \times 100\% $
Now, we have to find the value of y in the above equation in terms of x. We use the method of transposition to shift the terms in the equation and find the value of the variable. Keeping the variable on the right side of the equation and constants to the left side of the equation, we get,
$ \Rightarrow 50\% \times \dfrac{x}{{100\% }} = y$
Simplifying the calculations by cancelling common factors in numerator and denominator, we get,
$ \Rightarrow y = \dfrac{x}{2}$
So, $50\% $ of x is equal to $\dfrac{x}{2}$.
Hence, Meenal’s salary $ = x + \dfrac{x}{2}$
$ = \dfrac{{3x}}{2}$
Now, we have the difference between Ayushi’s salary and Meenal’s salary as $\dfrac{x}{2}$ rupees.
So, to find the percentage by which Ayushi’s salary is less than that of Meenal, we have the formula: $Percentage = \dfrac{{Part}}{{Whole}} \times 100\% $.
So, the whole corresponds to the number $\dfrac{{3x}}{2}$ and the part corresponds to the number $\dfrac{x}{2}$ in this case. So, we substitute these known values in the above mentioned formula. So, we get,
\[Percentage = \dfrac{{\left( {\dfrac{x}{2}} \right)}}{{\left( {\dfrac{{3x}}{2}} \right)}} \times 100\% \]
Cancelling common factors in numerator and denominator, we get,
\[ \Rightarrow Percentage = \dfrac{1}{3} \times 100\% \]
\[ \Rightarrow Percentage = 33.33\% \]
Therefore, Ayushi’s salary is 33.33% less than that of Meenal’s salary.

Note:
We can also solve this problem by assuming Ayushi’s salary as $100x$.
Given Meenal’s salary is 50% more than Ayushi’s, so Meenal’s salary will be $100x + 50 x = 150x$.
Ayushi's salary is $50x $ less than Meenal’s salary $150x$.
We need to tell this in percentages.
Ayushi salary difference w.r.t. Meenal’s salary, $\dfrac{50x}{150x} \times 100$
$= \dfrac{1}{3} \times 100 = 33.33 \%$
This is the required answer.