Question

In an examination, $5\% $ of the applicants were found ineligible and $85\% $ of the eligible candidates belonged to the general category. If $4275$ eligible candidates belonged to other categories, then how many candidates applied for the examination?

Answer 1

Hint: Let the total candidates be $x$ and then reduce the percentage of candidates that were ineligible, were from general category and another category. A percentage is a number or proportion that can be communicated as a small amount of $100$.

Formula used: Basic formula of percentage will be used and we will be subtracting each percentage from the total.
x% of y = $\dfrac{x}{y} \times 100$
Complete step by step answer:
Assuming that the number of candidates which are applying for the examination be $x$
In which $5\% $ of candidate found ineligible
$\therefore $ the percentage of eligible candidate =$100\% - 5\% $
=$95\% $
Total eligible candidate= $\dfrac{{95}}{{100}}x$
As provided in the question $85\% $ of the eligible candidates belonged to the general category
so, we will subtract this percentage in order to find out the percentage of eligible candidates from another category.
$\therefore $ the qualified competitors had a place with different classifications =$100\% - 85\% $
   =$15\% $
Hence total candidate belongs to other categories
= $\left( {\dfrac{{95}}{{100}}x} \right) \times \left( {\dfrac{{15}}{{100}}} \right)$
As given total candidate belonging to the other categories =$4275$
$\left( {\dfrac{{95}}{{100}}x} \right) \times \left( {\dfrac{{15}}{{100}}} \right)$​=$4275$
Now we will calculate for $x$ by keeping the variable $x$ at one side and taking rest constants on the other side.
$x$=$\dfrac{{4275 \times 100 \times 100}}{{95 \times 15}}$
on further calculating we get the value of $x$as;
$x = 30000$
Therefore, the total number of candidates who applied for the examination is equal to $30000$.

Note:
While solving, keep in mind the exact percentage that needs to be subtracted and from which it needs to be subtracted. And also make the calculations correct to avoid the errors and try to keep the work clean so that you do not need to solve the whole question again if you encounter a mistake.