Class 10th in a school has two sections, A and B. The average marks of section A is 50 and that of section B is 80. The combined average of the class is 65. Find the number of students in section A if there are a total of 60 students in the class.
Explanation:
Let the number of students in section A be x and in section B = (60 - x)
Then, (50 × x + 80 × (60 - x))/60 = 65
⇒ 50x + 4800 – 80x = 3900
⇒ 900 = 30x
⇒ x = 30
Alternately,
Here, the weighted average of the two section is same as the simple average of averages. That is possible only when the number of students (i.e. the weights) are same in both the sections.
Hence, both the section has same number of students, i.e. number of students in section A = 60/2 = 30.
Hence, option (d).
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