In a class of 100 students there are 70...

MathematicsMeasures of Central Tendency (Mean, Median, Mode)JEE Main 2002Easy

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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 marks of the girls?

(A)

(B)

(C)

(D)

Answer:B

Visualized Solution (English)

Visualizing the Class Split

Total Students in class = $100$
Number of Boys = $70$
Average marks of Boys = $75$
Average marks of complete class = $72$

The Total Marks Principle

Core Concept: $Total Marks = Average \times Number of Students$
Total Class Marks = Boys' Total Marks + Girls' Total Marks

Calculating Total Class Marks

Total marks for the complete class = $72 \times 100$
Total class marks = $7200$

Calculating Total Marks of Boys

Total marks for $70$ boys = $75 \times 70$
Total marks for boys = $5250$

Finding Total Marks of Girls

Total marks of girls = Total class marks - Boys' total marks
Total marks of girls = $7200 - 5250 = 1950$

Determining the Number of Girls

Number of girls = Total students - Number of boys
Number of girls = $100 - 70 = 30$

Calculating the Girls' Average

Average marks of girls = $\frac{Total marks of girls}{Number of girls}$
Average marks of girls = $\frac{1950}{30} = 65$

Summary and Reflection

Key Takeaway: Total sum is additive, while averages are not.
Final Answer: The average marks of the girls is 65.
Challenge: How would the average change if there were $50$ boys and $50$ girls?

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