A class consists of 20 boys and 30 girls. In the mid-semester examinat

Let the average score of the boys in the mid-sem exam be x; the average score of the girls in the mid-sem exam will then be (x+5).
Let the average score of the entire class in the mid-sem exam be k. We can draw the alligation diagram considering these values to look like the following:



From the diagram, we see that k = x+3.

In the final exam, the average scores of the girls reduced by 3 to become (x+2), while the average score of the entire class increased by 2 to become (x+5). Plugging these values in a NEW alligation diagram and solving for the variables, we see that the average score of the boys in the final exam is x+9.5.



Therefore, average score of the boys increased by 9.5. The correct answer option is B.

Most questions related to the concept of Weighted averages can be solved using the Alligation diagram in shorter time. So, please practice drawing the diagram by solving as many questions as possible on the topic of Weighted Averages, Alligation and Mixtures.

Here’s a link to one of our Webinars that we conducted on Mixtures and Alligation, for your reference.

https://bit.ly/2UEgZLX

Hope that helps!