Question

In a class, in an examination in Mathematics, 10 students scored 100 marks each, 2 students scored zero and the average of the remaining students is 72 marks. If the class average is 76, then the number of students in the class is:

• A. $44$
• B. $40$
• C. $38$
• D. $34$
• E. $32$

Hint:

For weighted average problems, the "deviation method" can be faster. The total deviation from the mean must be zero. The 10 students are +24 each ($+240$), the 2 students are -76 each ($-152$), so the remaining students must balance the $+88$ surplus by being 4 marks below the average ($72-76 = -4$). $88/4 = 22$ remaining students. Total $= 22 + 12 = 34$.

Answer 1

The Correct Option is D

Concept: The total marks in a class is equal to the number of students multiplied by the class average. This total is also the sum of the marks of all individual groups of students.

Step 1: Define the variables and set up the total marks equation.
Let the total number of students in the class be $n$.
• Students with 100 marks: $10$
• Students with 0 marks: $2$
• Remaining students: $n - (10 + 2) = n - 12$

Step 2: Calculate total marks using both methods.
Method 1 (Class average): Total marks $= 76 \times n$. Method 2 (Sum of groups): Total marks $= (10 \times 100) + (2 \times 0) + (n - 12) \times 72$.

Step 3: Equate and solve for $n$.
\[ 76n = 1000 + 0 + 72(n - 12) \] \[ 76n = 1000 + 72n - 864 \] \[ 76n - 72n = 136 \] \[ 4n = 136 \quad \Rightarrow \quad n = 34 \]