The average score of boys in the examination of a school is 71 and that of the girls is 73.The average score of the school in the examination is 71.8.Find the ratio of the number of boys to the number of girls who appeared in the examination?

Question

Answer

Answer

Introduction:

In this problem, we are given the average scores of boys and girls in an examination, as well as the average score of the entire school. From this information, we need to find the ratio of the number of boys to the number of girls who appeared in the examination.

Given:

- Average score of boys = 71
- Average score of girls = 73
- Average score of the school = 71.8

Formula:

- Average = Sum of observations / Total number of observations
- Sum of observations = Average x Total number of observations

Solution:

Let the number of boys who appeared in the examination be x and the number of girls who appeared in the examination be y.

Finding the sum of scores:

- Sum of scores of boys = 71x
- Sum of scores of girls = 73y
- Sum of scores of the entire school = 71.8(x + y)

Finding the ratio:

We can use the given averages to form two equations:
- 71 = (Sum of scores of boys) / x
- 73 = (Sum of scores of girls) / y

We can rearrange these equations to get:
- Sum of scores of boys = 71x
- Sum of scores of girls = 73y

We can substitute these values into the equation for the sum of scores of the entire school:
- 71.8(x + y) = 71x + 73y

Simplifying this equation, we get:
- 71.8x + 71.8y = 71x + 73y
- 0.8x = 1.2y
- x/y = 1.5/1

Therefore, the ratio of the number of boys to the number of girls who appeared in the examination is 1.5:1.

Conclusion:

The ratio of the number of boys to the number of girls who appeared in the examination is 1.5:1.

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