Question : The average score in an English exam of a class of 45 students in a coaching centre is 52. A group of 6 boys having an average score of 40 leave the class and another group of eight boys having an average score of 43 join the class. What is the new average score of the class?
Option 1: 48
Option 2: 53
Option 3: 49.5
Option 4: 52
Correct Answer: 52
Solution :
We know, Average = $\frac{\text{Sum of all the scores of the students}}{\text{No. of students}}$
The sum of the scores of all 45 students = Average × No. of students = 52 × 45 = 2340
Now, A group of 6 boys leaving the class, the average score is 40
⇒ Sum of the scores of 6 boys = Average × No. of students = 40 × 6 = 240
⇒ Sum of the scores of 8 boys joining the class = Average × No. of students = 43 × 8 = 344
Now, the average score of the class
$=\frac{\text{Total Sum - Sum of scores of students leaving class + Sum of scores of students joining class }}{\text{Total number of students - Number of students leaving + number of students joining}}$
$=\frac{2340-240+344}{45-6+8}=\frac{2444}{47}=52$
Hence, the correct answer is 52.
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