Average of the height of 286 students of a school is 50 unit. If the average of the height of the boys is 53 unit and the average of the height of the girls is 31 unit, then what will be the ratio of the total height of boys and the total height of girls respectively ?

1007 : 93

Total height of the students = 286 x 50 

Let number of boys be x,

number of girls = 286 -  x

Height of all boys = 53x

Height of all girls = 31 x (286 - x) 

According to the question,

53x + 31 x (286 - x)  = 286 x 50

⇒  22x  = 286(50 - 31)

⇒  22x  = 286 x 19

⇒     x  = 247

Number of girls = 286 - 247 = 39

Height of boys = 53 x 247

Height of girls = 31 x 39

Ratio = 1007  :  93