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The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
1. 80%
2. 60%
3. 40%
4. 20%

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Correct Answer - Option 1 : 80%

Concept:

The average marks = \(\rm \text{Sum of marks of all the students}\over \text{Total number of students}\)

Calculation:

Given the avg. marks of boys = 52 and that of girls = 42

Let the no. of boys be x and of girls be y

Sum of marks of boys = 52 x

Sum of marks of girls = 42 y

According to the question, if 50 is the combined average;

⇒ 52x + 42y = 50(x + y)

⇒ 52x + 42y = 50x + 50y

⇒ 2x = 8y

∴ x = 4y

Total number of students in the class = x + y = 4y + y = 5y

 % of boys = \(\rm \frac{\text{No of boys}}{\text{Total No. of students}} \times 100\)

\(\rm \frac{4y}{5y} \times 100\)

= 80%

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