Question

In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls?

• A. $73$
• B. $85$
• C. $68$
• D. $74$
• E. $65$

Hint:

Always convert averages into total sums first—this avoids mistakes.

Answer 1

The Correct Option is C

Concept: \[ \text{Average} = \frac{\text{Total Sum}}{\text{Number of observations}} \]

Step 1: Total students \[ \text{Total} = 100, \text{Boys} = 70 \Rightarrow \text{Girls} = 30 \]

Step 2: Total marks of boys \[ \text{Average} = 75 \Rightarrow \text{Total marks} = 70 \times 75 = 5250 \]

Step 3: Total marks of whole class \[ \text{Average} = 72 \Rightarrow \text{Total marks} = 100 \times 72 = 7200 \]

Step 4: Total marks of girls \[ = 7200 - 5250 = 1950 \]

Step 5: Average of girls \[ = \frac{1950}{30} = 65 \] \[ \boxed{65} \]