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

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Solution

Let the number of boys = x and the number of girls = y.
Boys get a mean of 70 marks.
Mean marks for boys = total marks for boys/number of boys
so 70 = total marks for boys/x or total marks for boys = 70x
Mean marks for girls= total marks for girls/number of girls
so 73= Total marks for girls /y or total marks for girls = 73y
Mean marks for all students = (total marks for boys+total marks for girls)/(number of boys +number of girls)
or 71= (70x+73y)/(x+y) Cross-multiply
71(x+y) = 70x+73y
71x+71y= 70x+73y
x = 2y
It means the ratio of number of boys to number of girls is 2 :1
Answer: 2:1

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