The mean marks (out of 100) of boys and girls in an examinatin are 70 and 73, respectively. If the sum mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

The mean marks (out of 100) of boys and girls in an examinatin are 70

1.	The mean marks (out of 100) of boys and girls in an examinatin are 70 and 73, respectively. If the sum mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Answer» Let x and y be the number of boys and girls, respectively. Given, mean marks (out of 100) of boys `(barx_(1))=70` and mean marks (out of 100) of girls `(barx_(2))` =73 Also, given that, mean marks of all the students in the exmaination `(barx_(12))=71` Now, using the formula, Combined mean , `(barx_(12))= (barx_(1)n_(1)+barx_(2)n_(2))/(n_(1)+n_(2))=71` (Given) `therefore (70n_(1) + 73n_(2))/(n_(1)+n_(2))=71` `rArr 70n_(1)+73n_(2)= 71n_(1)+71n_(2)` `rArr 73n_(2)-71n_(2)=71n_(1)-70n_(1)` `rArr 2n_(2)=n_(1)` `rArr n_(1)/n_(2)=2/1 or n_(1):n_(2)=2:1`