Question

The salary of Ramesh is $25\% $ more than that of Anil’s salary. By what percentage is Anil’s salary less than that of Ramesh’s?

Answer 1

Hint: First, we need to know about the concepts of the percentage, so that we are able to solve the given problem easily. The percentage is the mathematical concept which is to measure the proportion of the given values in any term of the original value. The percentage is a relative value that indicates the hundredth parts of any quantity.
Like $70\% $ of $40$ is $28$. This can be obtained by $40 \times \dfrac{{70}}{{100}} = 28$ where $70$ represents the percent, $40$ is the base, and $28$ is the part.
Formula used: If a number is $x\% $ more than the other, then the other number is less than the first number, which can be calculated using the formula, $\dfrac{x}{{100 + x}} \times 100$.

Complete step-by-step solution:
Since from the given that we are asked to find in what percentage is Anil’s salary less than that of Ramesh’s salary.
Also given that the salary of Ramesh is $25\% $ more than that of Anil’s salary.
We know the formula to obtain more than a percentage given above. Also, we know that from given, salary of Ramesh is $25\% $ more than that of Anil’s salary, and hence to find the is Anil’s salary less than that of Ramesh’s salary is by substituting the unknown value $x\% = 25\% $ in the given formula.
Thus, we have $\dfrac{x}{{100 + x}} \times 100 = \dfrac{{25}}{{100 + 25}} \times 100$
By the addition operation, we have $\dfrac{{25}}{{125}} \times 100$
By the division operation, we get $\dfrac{{25}}{{125}} \times 100 = \dfrac{1}{5} \times 100$
Again, from division we have $\dfrac{{100}}{5} = 20$
Hence $20\% $ percentage is Anil’s salary less than that of Ramesh’s salary.

Note: The operations which we used in the solutions are addition and division.
The addition operation is the sum of the given two or more than two numbers and which obtains a new resultant number from the sum. The division is the inverse process of the multiplication which has a dividend and divisor. Also, we get the remainder while dividing the given two numbers.