Question

In an examination, 72% of the total examinees passed. If the number of failures is 392, find the total number of examinees.

Answer 1

Hint: We know that percentage is a number or fraction that is expressed as a fraction of 100. We are also aware that the total percentage is 100% , i.e., percentage is a number out of 100. For each candidate, passing or failing are the only possible options. So, if 72% passed, then we can say that 28% failed. We can equate this quantity with 392, to get the total number of examinees.

Complete step-by-step solution:
Let the total number of examinees be $x$ .
We know that each examinee could either pass or fail the examination. There is no other possibility.
We are also aware that the percentage is the quantity out of 100. So if 72% examinees passed the examination, then we can easily infer that (100 – 72)%, i.e., 28% examinees failed the examination.
But, in our question, we are given that the total number of examinees who failed the examination is 392. Thus, we can write
$28\%\text{ of }x=392$
Using the definition of percentage, we have
$\dfrac{28}{100}\times x=392$
We can rearrange the terms to get the value of $x$ ,
$x=\dfrac{392\times 100}{28}$
Thus, we get
$x=1400$
Hence, the total number of examinees is 1400.

Note: We can also use the concept of unitary method to solve this problem. If 28% of examinees is 392, then we know that 1% of examinees will be equal to $\dfrac{392}{28}$ , i.e., 14. So, 100% of the examinees will be equal to $14\times 100$ , i.e., 1400. So, we can say that the total number of examinees must be 1400.