Answer
Verified
376.8k+ views
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.
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE