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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