Question

The salary of Sachin Tendulkar is 25% more than that of Ricky Ponting. By what percentage is Ricky’s salary less than that of Sachin’s?

Answer 1

Hint: We will first let the salary of Ricky be $x$. Then, find the difference in the salaries of Ricky and Sachin by using the given conditions. Apply the formula ${\displaystyle \frac{\text{Difference in salaries}}{\text{Sachin's salary}}}\times 100$ to find the percentage by which Ricky’s salary is less than that of Sachin’s.

Complete step-by-step answer:
Let us assume that the Ricky’s salary is $x$
Then, according to the question, we can write,
Sachin’s salary is $x+{\displaystyle \frac{25}{100}}x$
Which can be simplified as,
$$\begin{gathered} =x+{\displaystyle \frac{1}{4}}x \\ ={\displaystyle \frac{5x}{4}} \end{gathered}$$
We will now find the difference between Ricky's salary and Sachin’s salary.
That is, we will subtract $x$ from ${\displaystyle \frac{5x}{4}}$
$$\begin{gathered} ={\displaystyle \frac{5x}{4}}-x \\ ={\displaystyle \frac{5x-4x}{4}} \\ ={\displaystyle \frac{x}{4}} \end{gathered}$$
Hence, Ricky's salary is ${\displaystyle \frac{x}{4}}$ less than Sachin's salary.
But we have to find out how much percent Ricky’s salary is less than Sachin’s salary.
Ricky’s salary is less than Sachin’s salary by ${\displaystyle \frac{\text{Difference in salaries}}{\text{Sachin's salary}}}\times 100$
Therefore we get,
$$\begin{gathered} \Rightarrow {\displaystyle \frac{{\displaystyle \frac{x}{4}}}{{\displaystyle \frac{5x}{4}}}}\times 100 \\ \Rightarrow {\displaystyle \frac{x}{4}}\times {\displaystyle \frac{4}{5x}}\times 100 \\ \Rightarrow {\displaystyle \frac{1}{5}}\times 100 \\ \Rightarrow 20\mathrm{\%} \end{gathered}$$
Thus, Ricky’s salary less than that of Sachin’s by 20%


Note: We were to find the percentage by which Ricky’s salary is less than that of Sachin’s, therefore, we have to write Sachin’s salary in the denominator. Many students make mistakes by taking Ricky’s salary in the denominator.