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# Two numbers are respectively $30$ percentage and $40$ percentage less than a third number. What percent is the second less of the first?

Last updated date: 14th Jul 2024
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Hint: To get the required percentage, we will consider a variable for third number and will find the first two numbers in respect to the third number by using the given condition in the question that first number is $30$ percentage less than a third number and second number is $40$ percentage less than a third number. Then, we will divide the second number to the first number and will multiply with $100$ to get the answer.

Let’s consider that the third number is $x$.
Since, the first number is $30$ percentage less than a third number. So, the $30$percent of first number is:
$= x\times \dfrac{30}{100}$
After required calculation, we will have:
$= \dfrac{3x}{10}$
Now, the second number will be:
$= x-\dfrac{3x}{10}$
Here, we will use the method of subtraction of fraction as:
$= \dfrac{10x-3x}{10}$
We will have $7$ after subtracting $3$ from $7$ as:
$= \dfrac{7x}{10}$
And the third number is $40$ percentage less than the third number. So, $40$ percentage of a number is:
$= x\times \dfrac{40}{100}$
After required calculation, we will have:
$= \dfrac{4x}{10}$
Now, the third number will be:
$= x-\dfrac{4x}{10}$
Here, we will use the method of subtraction of fraction as:
$= \dfrac{10x-4x}{10}$
We will have $6$ after subtracting $4$ from $10$ as:
$= \dfrac{6x}{10}$
Now, we will get the required percentage as:
$=\dfrac{\text{second number}}{\text{first number}}\times 100$
Substituting the relative values in the above step as:
$=\dfrac{\dfrac{6x}{10}}{\dfrac{7x}{10}}\times 100$
Now, we will cancel out the equal like terms as:
$=\dfrac{6}{7}\times 100$
After multiplication of numerator with $100$, we will have the above step as:
$=\dfrac{600}{7}\%$
After doing appropriate calculations, we will have the required percentage as:
$= 85\dfrac{5}{7}\%$
Hence, $85\dfrac{5}{7}$percent is the second less of the first.

Note: We can do this question in the terms of percentage as:
Let’s consider that the third number is $100$ percentage.
Then according to the given condition the second number is$30$ percentage less than third number. So, the second number would be:
$= \left( 100-30 \right)$ Percentage
$= 70$ Percentage
Since, the second number is less than $40$ percentage less than the third number. Similarly, the second number will be as:
$= \left( 100-40 \right)$ Percentage
$= 60$ Percentage
Now, the required percentage is:
$= \dfrac{60}{70}\times 100$
After doing necessary calculations, we will get:
$= 85\dfrac{5}{7}\%$
Since, we got the same percentage as the solution. Hence, the solution is correct.