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
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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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