# The average of marks obtained by $120$ candidates was $35$. If the average of the passed candidates was $39$ and that of the failed candidates was $15$, then find the number of those candidates who passed the examination.A) $120$ B) $110$ C) $100$ D) $150$

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Hint: First we have to find the total number of marks obtained by $120$ students which is=total number of candidates × average marks. Then assume the number of passed students to be x so failed students will be $120 - {\text{x}}$ . Now find the number obtained by passed and failed students and add them which will be equal to the total marks obtained. Solve for x and you’ll get the answer.

Given, the total number of candidates=$120$ and the average of marks by those candidates=$35$ Then,
The total number of marks obtained by $120$ students= total number of candidates × average marks of those students=$120 \times 35 = 4200$
Also, given that the average marks obtained by passed students=$39$ and the average marks obtained by failed students=$15$. We have to find the number of passed candidates.
Let us assume the number of passed students to be x. Since the total number of students is $120$. So the number of failed students=$120 - {\text{x}}$
Then the total marks obtained by passed students = total number of passed candidates × average marks of those students=$39 \times {\text{x = 39x}}$
And the total marks obtained by failed students= total number of failed candidates × average marks of those students=$\left( {120 - {\text{x}}} \right) \times 15 = 1800 - 15{\text{x}}$
We know that the marks obtained by passed candidates + marks obtained by failed students=total marks obtained by $120$ students. On putting the values, we get-
$\Rightarrow 39{\text{x + 1800 - 15x = 4200}}$
On separating the variable and constants, we get-
$\Rightarrow 39{\text{x - 15x = 4200 - 1800}}$
On solving further, we get-
$\Rightarrow 24{\text{x = 2400}} \\ \Rightarrow {\text{x = }}\dfrac{{2400}}{{24}} = 100 \\$
So the number of passed candidates=$100$.
Hence the correct answer is ‘C’.

Note: Here the students may get confused in finding the total marks obtained by $120$ students. We know the formula of average is-Average marks= $\dfrac{{{\text{total marks obtained}}}}{{{\text{Total number of students}}}}$
We know the number of students and the average marks. So we find the total number of marks by multiplying the total number of students to the average marks of those students.