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  • 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 number of boys to the number of girls.

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 number of boys to the number of girls.

Answers (1)

Answer :  [ 2:1 ]

Let the no. of boys and girls be x and y respectively.

 \text{ Mean }=\frac{\text { sum of observations}}{\text {Number of observations}}

Now, mean marks of x boys in the examination =70

Sum of marks of x boys =70 x

Mean marks of y girls in the examination =73

Sum of marks of y girls =73y

Given, mean marks of all students (x + y) = 71

Sum of marks of all students (x + y) = 71(x + y)

Now, sum of marks of all students x + y =sum of marks of x boys and sum of marks of y girls

\\71(x + y) = 70x + 73 y\\ 71x + 71y = 70x + 73y\\ 71x - 70x = 73y- 71y\\ x = 2y

\frac{x}{y}=\frac{2}{1}

Hence, the ratio is x:y=2:1

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