The average score of girls in a class 'X' examination in a school is 73 and that of boys is 71.The average score is class X of that school is 71.8.Find the percentage of the number of girls and boys in a class x of the school:40% and 60%30% and 60%20% and 40%40% and 80%

To solve this problem, we need to use the formula for a weighted average. The weighted average is given by:

(weight1 * value1 + weight2 * value2) / (weight1 + weight2)

Here, the weights are the percentages of girls and boys in the class, and the values are their respective average scores. We know that the overall average score is 71.8.

Let's denote the percentage of girls as 'g' and the percentage of boys as 'b'. We can then write the equation as follows:

(73g + 71b) / (g + b) = 71.8

We also know that the sum of the percentages of girls and boys must be 100%, so we have another equation:

g + b = 100

We now have a system of two equations, which we can solve to find the values of 'g' and 'b'.

However, since the options are given, we can also try to plug in the options into the first equation and see which one gives us the correct average score.

Let's try the first option: 40% girls and 60% boys.

(730.4 + 710.6) / (0.4 + 0.6) = 71.8

So, the first option is the correct answer. The percentages of girls and boys in the class are 40% and 60% respectively.

To solve this problem, we can use the formula for a weighted average. The weighted average is given by:

(weight1 * value1 + weight2 * value2) / (weight1 + weight2)

In this case, the weights are the percentages of girls and boys in the class, and the values are their respective average scores. We know that the overall average score is 71.8.

Let's denote the percentage of girls as 'g' and the percentage of boys as 'b'. We can then write the equation as follows:

(73g + 71b) / (g + b) = 71.8

We also know that the sum of the percentages of girls and boys must be 100%, so we have another equation:

g + b = 100

We can solve this system of equations to find the values of 'g' and 'b'. However, since the question provides us with multiple choices, we can also try each of them and see which one satisfies both equations.

1. 40% and 60%: (730.4 + 710.6) / (0.4 + 0.6) = 71.8, so this choice is correct.
2. 30% and 60%: (730.3 + 710.6) / (0.3 + 0.6) = 71.1, so this choice is incorrect.
3. 20% and 40%: (730.2 + 710.4) / (0.2 + 0.4) = 71.6, so this choice is incorrect.
4. 40% and 80%: (730.4 + 710.8) / (0.4 + 0.8) = 71.6, so this choice is incorrect.

Therefore, the correct answer is 40% and 60%.