Question : The average weight of some students in a class was 60.5 kg. When 8 students, whose average weight was 65 kg, joined the class, then the average weight of all the students increased by 0.9 kg. The number of students in the class, initially, was:
Option 1: 37
Option 2: 42
Option 3: 32
Option 4: 40
Correct Answer: 32
Solution :
Let the total number of students be $x$.
Average weight of $x$ students = 60.5 kg
The sum of the weights of $x$ students = $60.5x$ kg
The average weight of 8 students = 65 kg
The sum of the weights of 8 students = 65 × 8 = 520 kg
According to the question,
$⇒60.5x + 520 = (x + 8)(60.5 + 0.9)$
$⇒60.5x + 520 = (x + 8) × 61.4$
$⇒60.5x + 520 = 61.4x + 491.2$
$⇒61.4x - 60.5x = 520 - 491.2$
$⇒0.9x = 28.8$
$⇒x = 32$
Hence, the correct answer is 32.
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