Question

The salary of Sachin Tendulkar is 20% more than that of Ricky Ponting. By what percentage is Ricky’s salary less than that of Sachin’s)
 (Write answer in the nearest integer)

Answer 1

Hint: Take Ricky’s salary as x. So, according to question, Sachin's salary would be \[x + \dfrac{{20x}}{{100}} \Rightarrow \dfrac{{120x}}{{100}} \Rightarrow \dfrac{{6x}}{5}.\]Then, calculate difference in salary to get the desired result.

Complete step-by-step answer:
In the question, we are told that, the salary of Sachin Tendulkar is 20% more than that of Ricky Ponting, so, we have to tell that, by what percent is Ricky’s salary less than that of Sachin's.
In the expression % is called percentage. At first, we will learn about this term percentage.
In mathematics, a percentage (from Latin per centum "by a hundred") is a number of ratios expressed as a fraction of 100. It is often denoted by using the '%' sign or the abbreviation "pct.", "pct" sometimes "pc" is also used. A percentage is dimensionless or pure number.
For example: 45% is read as forty-five percent is equal to \(\dfrac{{45}}{{100}} \Rightarrow 0.45\)
The term percent is derived from the Latin per centum meaning "by the 100". The sign for "percent" evolved by a gradual can't ration of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p" and eventually disappeared entirely. The word "cento" was contracted to two circles separated by horizontal lines, from which modern "%" is derived.
Let's suppose that the salary of Ricky Ponting is 'x'. Now, in the question, it is said that the amount of Sachin's salary is 20% more than Ricky Pointing's salary. So, according to question, we can say that, Sachin's salary is more than Ricky’s salary by 20% \( \Rightarrow \dfrac{{20}}{{100}} \times x\) which can be written as \(\dfrac{x}{5}.\) So, the salary of Sachin will be \(x + \dfrac{x}{5} \Rightarrow \dfrac{{5x + x}}{5}\) which can be said as \(\dfrac{{6x}}{5}\) if Ricky’s salary is x.
Now, here the percentage will be upon Sachin's salary. So, the difference between the salary of Sachin and Ricky is \(\dfrac{{6x}}{5} - x \Rightarrow \dfrac{x}{5}\)
The percentage by which Ricky’s salary is less than that of Sachin's is \(\dfrac{{\dfrac{x}{5}}}{{\dfrac{{6x}}{5}}} \times 100\% \Rightarrow \dfrac{1}{6} \times 100\% \) which can be calculated as 16.66% and approximate as 17%.
Therefore, the percentage is 17%.

Note: This question can also be solved by another way. We can find the difference by calculating 20% of Ricky’s salary and then calculating its percentage upon Sachin's salary like this,
\(\dfrac{{\left( {{\rm{Difference\ between\ Sachin\ and\ Ricky's\ salary}}} \right)}}{{{\rm{Sachin's\ salary}}}} \times 100\)