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02 Apr 2020, 10:23
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Difficulty:
65%
(hard)
Question Stats:
63% (03:03) correct
37%
(03:10)
wrong
based on 186
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A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is:
A. 10
B. 9.5
C. 9
D. 6
E. 4.5
A. 10
B. 9.5
C. 9
D. 6
E. 4.5
02 Apr 2020, 18:48
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let,In the mid-semester examination, total score of girls = x and score of boys = y
so, x/30 = y/20 + 5
Average score of class = (x + y)/ 50
In the final exam,total score of girls = (x/30 – 3)*30
Total score of class = ((x + y)/ 50 +2 )*50
therefore,Total score of boys = [((x + y)/ 50 +2 )*50 - (x/30 – 3)*30 ]
or, average of boys =[((x + y)/ 50 +2 )*50 - (x/30 – 3)*30 ]/20 = (y + 190)/20 = y/20 + 9.5
So, average of boys increases by 9.5
correct answer is B
so, x/30 = y/20 + 5
Average score of class = (x + y)/ 50
In the final exam,total score of girls = (x/30 – 3)*30
Total score of class = ((x + y)/ 50 +2 )*50
therefore,Total score of boys = [((x + y)/ 50 +2 )*50 - (x/30 – 3)*30 ]
or, average of boys =[((x + y)/ 50 +2 )*50 - (x/30 – 3)*30 ]/20 = (y + 190)/20 = y/20 + 9.5
So, average of boys increases by 9.5
correct answer is B
03 Apr 2020, 03:13
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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:
03rd Apr 2020 - Reply 5 - 1.jpg [ 52.66 KiB | Viewed 11130 times ]
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.
03rd Apr 2020 - Reply 5 - 2.jpg [ 58.3 KiB | Viewed 11028 times ]
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!
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:
Attachment:
03rd Apr 2020 - Reply 5 - 1.jpg [ 52.66 KiB | Viewed 11130 times ]
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.
Attachment:
03rd Apr 2020 - Reply 5 - 2.jpg [ 58.3 KiB | Viewed 11028 times ]
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!
