Question

What is the total number of candidates at an examination if \[31\% \] fail and the number of those who passed exceeds the number of those who failed by \[247?\]

Answer 1

Hint: First thing we have given is the percentage of failed candidates is \[31\% \] to use this we calculate the percentage of pass candidates.
Now, in this question, the second thing we have given is the difference between failed candidates marks and passed candidates marks is \[247\] and then after solving it we find out the total number of candidates .

Complete step-by-step answer:
Let the total number of candidates be \[x\].
It is given that the Percentage of failed candidates \[ = 31\% \]
Percentage of passed candidates \[ = 69\% \] \[\] \[(100\% - 31\% )\]
First of all we have to calculate the candidates marks because we are also given the difference between failed candidates marks and passed candidates marks is \[247\] .
To find candidates marks we use following formula as:
Candidate Marks \[ = Percentage * TotalMarks\]
As we are given with,
Difference between failed candidates marks and passed candidates marks is \[247\]’
So, it is written as \[69\% of x - 31\% of x = 247\]
After converting into equation,
$\Rightarrow$ \[\begin{array}{l}\dfrac{{69x}}{{100}} - \dfrac{{31x}}{{100}} = 247\\\end{array}\]
On taking L.C.M we get,
$\Rightarrow$ \[\dfrac{{38x}}{{100}} = 247\]\[\]
Taking 100 on right hand side in multiplication we get,
$\Rightarrow$ \[38x = 24700\]
Taking 38 in left hand side in dividing we get,
$\Rightarrow$ \[x = \dfrac{{24700}}{{38}}\]
On simplifying we get the value of x that is,
$\Rightarrow$ \[x = 650\]
Therefore, the total number of candidates \[ = 650\]
Hence, we can easily calculate the total number of candidates .

 Note: Read the question carefully because when given in a question is one variable
 is exceed by another one variable by some quantity then it means we have
to calculate the difference between two variables . Remember one basic thing is total percentage is \[100\% \] because when variable percentage is given then we calculate the other variable percentage by subtracting from \[100\% \] .