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

Solution :

Let the number of boys and girls be x and y, respectively

\(\therefore\)   52x + 42y = 50(x + y)

\(\implies\)  52x + 42y = 50x + 50y

\(\implies\)  2x = 8y

\(\implies\)  x = 4y

\(\therefore\)  Total number of students in the class

= x + y = 4y + y = 5y

\(\therefore\)  Required number of boys

= \(4y\over 5y\) \(\times\) 100% = 80%

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