Question : The total number of students in sections A and B of a class is 72. The ratio of the number of students in A and B is 7 : 5. The average weight (in kg) of the students in section B is 20% more than that of the students in section A. If the average weight of all the students in the class is 52 kg, then what is the average weight (in kg) of the students in section B?
Option 1: 57.6
Option 2: 57.9
Option 3: 56.4
Option 4: 58.2
Correct Answer: 57.6
Solution :
Let the number of students in sections A and B be 7 and 5 respectively.
Let the average weight of section A be $5x$.
Average weight of section B = $5x × (\frac{6}{5}) = 6x$
Average = $\frac{\text{Sum of all the observations}}{{\text{Total number of observations}}}$
According to the question,
$⇒7 × 5x + 5 × 6x = 12 × 52$
$⇒35x + 30x = 12 × 52$
$⇒65x = 12 × 52$
$⇒x = 9.6$
Average weight of section B = 9.6 × 6 = 57.6 kg
Hence, the correct answer is 57.6.
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