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Question : The numbers of students in section A and section B of a class are 50 and 62, respectively. The average score in mathematics of all the students is 75. If the average score of students in section A is 20% more than that of students in section B, then what is the average score of students in section A (correct to one decimal place)?

Option 1: 87.5

Option 2: 82.6

Option 3: 84.3

Option 4: 85.7


Team Careers360 2nd Jan, 2024
Answer (1)
Team Careers360 18th Jan, 2024

Correct Answer: 82.6


Solution : Let the average score of students in section B be A B ​ and the average score of students in section A be  A A​
So,  A A ​= A B ​+ 0.2 × A B = 1.2 × A B​
Total Score in A = 50 × A A ​ = 50 × 1.2 × A B​
Total Score in B = 62 × A B
Now, Overall Average = $\frac{\text{Sum of the scores obtained by all students}}{\text{Total Number of Students}}$
⇒ 75 = $\frac{50×A_A​+62×A_B​​}{50+62}$ = $\frac{50×(1.2×A_B​)+62×A_B}{​​112}$
⇒ A B = $\frac{75×112}{122}$ = 68.85
So, A A = 1.2 × 68.85 = 82.6
Hence, the correct answer is 82.6.

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