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

Let the number of boys and girls be x and y respectively.

We know that, Sum of observations = Mean × Number of observations

Given, Mean marks of boys in the examination = 70

∴ Sum of marks obtained by boys in the examination = 70 × x = 70

Given, Mean marks of girls in the examination = 73

∴ Sum of marks obtained by girls in the examination = 73 × y = 73

Given, Mean marks of all students in the examination = 71

∴ Sum of marks obtained by all students in the examination = 71 (x + y)

Sum of marks obtained by all students in the examination

= Sum of marks obtained by boys in the examination + Sum of marks obtained by girls in the examination

∴ 71 (x + y) = 70x + 73y

⇒ 71x + 71y = 70x + 73y

⇒ 71x – 70x = 73y – 71y

x = 2y x : y = 2:1

Thus, the ratio of number of boys to the number of girls is 2 :1.

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