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

Let n1 and n2 be the number of boys and girls respectively in the class.We have X1¯=52,X2¯=42 and X¯=50∴ X¯=n1X1¯+n2X2¯n1+n2⇒ 50=52n1+42n2n1+n2⇒8n2=2n1⇒n1=4n2∴ Percentage of boys =n1n1+n2×100=4n25n2×100=80