The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the

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*x *

Given, Mean marks of girls in the examination = 73

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

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*) = 70*x* + 73*y*

⇒ 71*x* + 71*y* = 70*x* + 73*y*

⇒ 71*x* – 70*x* = 73*y* – 71*y*

⇒ *x* = 2*y*

⇒ *x* : *y* = 2:1

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

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