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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.

Solution:

Given, the mean marks of boys and girls in an examination are 70 and 73.

The mean marks of all the students in the examination is 71.

We have to find the ratio of the number of boys to the number of girls.

Mean = sum of observation / total observation

Let the number of boys be B

Let the number of girls be G

Mean marks of boys = 70

Total marks of boys = 70B

Mean marks of girls = 73

Total marks of girls = 73G

Mean marks of all the students = 71(B + G)

So, 71(B + G) = 70B + 73G

71B + 71G = 70B + 73G

71 B - 70B = 73G - 71G

B = 2G

Now, ratio of boys to girls = 2G/G

= 2/1

= 2 : 1

Therefore, the required ratio is 2 : 1

✦ Try This: The mean marks (out of 100) of boys and girls in an examination are 80 and 93, respectively. If the mean marks of all the students in that examination is 81, find the ratio of the number of boys to the number of girls.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 11

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

Summary:

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

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