Question

In an examination, $ 300 $ students appeared. Out of these students $ 28\% $ got first division, $ 54\% $ got second division and the remaining just passed. Assuming that no students failed, find the number of students who just passed.
 $ A)54 $
 $ B)50 $
 $ C)60 $
 $ D)55 $

Answer 1

Hint: First, we need to know about the percentage, which means a number or a given ratio will be represented in the form of fractions of $ 100 $
The percentage is the relative value that will indicate the hundredth parts of a given quantity.
Like $ 70\% .40 = 28 $ here, seventy is the percent and fourth is the base and twenty-eight is the part.
A total of $ 300 $ appeared for the examination.

Complete step by step answer:
From the given that in the examination three are total three hundred students have appeared.
Hence the $ 300 $ students are the base for the percentage.
First, the number of students who got the first division rank is given as $ 28\% $
Now converting using the percentage rule that, $ 28\% $ of given $ 300 $ students is $ \dfrac{{28}}{{100}} \times 300 \Rightarrow 28 \times 3 $ (by the use of division and multiplication operation), hence we get $ 28 \times 3 = 84 $ students who got the first division overall.
Similarly, we find the second division rank is given as $ 54\% $ .
By the same method, thus we get $ \dfrac{{54}}{{100}} \times 300 = 54 \times 3 \Rightarrow 162 $ students who got the second division.
From the given, they said that no students failed on the exams.
Hence to get the number of students who have just passed (average of marks in the exam) we just need to calculate the total number of students and subtract the first and second divisions students.
Hence, we get $ 300 - (84 + 162) $ where the total number is subtracted to first and second division students to get the just passed students from above.
Thus, solving this we get, the number of just passed students will be $ 300 - (84 + 162) \Rightarrow 54 $
Hence a total of fifty-four students just passed.

So, the correct answer is “Option A”.

Note: If the failed students are also given, it is the same way of solving the problem like the total number of students subtracts the first division and second division and also the failed students, which is represented as $ T - (Fi + S + Fa) $ (where \[{F_i}\] is the first division and \[{F_a}\] is the failed student).
Since there is no possibility of getting the other options, if we get that then it will affect the question as like $ C)60 $ is correct, then we get $ 84 + 162 + 60 = 306 $ students in total.