Question

Ravi’s income is $25\% $ more than that of Raghu. What percent is Raghu’s income less than that of Ravi?

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 answer:
Since from the given that we are asked to find in what percent is Raghu’s income less than that of Ravi
Also given that the salary of Ravi is $25\% $ more than that of Raghu’s.
We know the formula to obtain more than a percentage given above. Also, we know that from given, salary of Ravi is $25\% $ more than that of Raghu’s income, and hence to find the is Raghu’s less than that of Ravi’s income 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 $\dfrac{{25}}{{125}} \times 100 \Rightarrow \dfrac{1}{5} \times 100$
Again, from division we have $\dfrac{{100}}{5} = 20$
Hence $20\% $ percent is Raghu’s income less than that of Ravi.

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 a divisor. Also, we get the remainder while dividing the given two numbers.