Answer

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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.

**Complete step by step 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.

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