Question

The average marks of 30 students in a class was 80. After two students left out of the class, the average marks of the remaining students was 82. Then the average marks of the two left out students is

• A. 62
• B. 72
• C. 70
• D. 52
• E. 60

Hint:

Shortcut Tip: Using deviations: The 28 remaining students gained $+2$ points each (from 80 to 82), so they "took" $28 \times 2 = 56$ points from the pool. Therefore, the 2 leaving students must have been 56 points below the original average. Average of leavers = $80 - (56 / 2) = 80 - 28 = 52$.

Answer 1

The Correct Option is D

Concept:
The average (mean) of a set of values is the sum of the values divided by the total number of values ($\text{Average} = \text{Sum} / N$). We can rearrange this to find the total sum: $\text{Sum} = \text{Average} \times N$. By finding the difference between the total sums before and after the students leave, we can determine the exact combined score of the departing students.

Step 1: Calculate the initial total marks.
The class originally had 30 students with an average of 80 marks. $$\text{Total Initial Sum} = 30 \times 80 = 2400$$

Step 2: Calculate the new total marks after students leave.
Two students left, meaning there are $30 - 2 = 28$ students remaining. Their new average is 82. $$\text{Total New Sum} = 28 \times 82 = 2296$$

Step 3: Find the combined marks of the leaving students.
The difference between the initial total and the new total represents the marks that "left" the room. $$\text{Sum of Left Students} = \text{Initial Sum} - \text{New Sum}$$ $$\text{Sum of Left Students} = 2400 - 2296 = 104$$

Step 4: Set up the final average calculation.
The question asks for the average marks of these two specific students, not their total. $$\text{Average of Left Students} = \frac{\text{Combined Marks}}{2}$$

Step 5: Perform the final division.
Divide the sum by 2: $$\text{Average} = \frac{104}{2} = 52$$ Hence the correct answer is (D) 52.