Question : The average mark of 50 students in a class is 72. The average marks of boys and girls in that subject are 70 and 75, respectively. The number of boys in the class is:
Option 1: 20
Option 2: 35
Option 3: 25
Option 4: 30
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Correct Answer: 30
Solution :
Average of 50 students = 72
Total score of 50 students = 72 $\times$ 50 = 3600
The total score of boys = 70$x$
Where $x$ is the number of boys in the class
⇒ Total score of girls = 75(50 – $x$)
According to the question,
70$x$ + 75(50 – $x$) = 3600
⇒ 70$x$ + 3750 – 75$x$ = 3600
⇒ 5$x$ = 150
$\therefore x$ = 30
$\therefore$ The number of boys in the class is 30
Hence, the correct answer is 30.
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