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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