The average weight of students in a class was 58.5 kg. When 8 more students with average weight of 64.5 kg joined the class, then the average weight of all the students increased by 0.96 kg. What was the number of students, initially, in the class?

Explanation

Given: Average weight of students in a class = 58.5 kg If 8 more students with average weight of 64.5 kg joined the class, then average weight of all the students increased by 0.96 kg Formula used: Average = Sum of the total weight of students/ Total number of students Calculation: Let the number of students initially in a class be x. Average = Sum of the total weight of students/ Total number of students 58.5 = Sum of the total weight of students/x Sum of the total weight of students = 58.5x If 8 more students with average weight of 64.5 kg joined the class then, 64.5 = Sum of the weight of 8 students/8 Sum of the weight of 8 students = 64.5 × 8 = 516 Now, After joining 8 students average weight increases 0.96 kg, then new average of total students = 58.5 + 0.96 = 59.46 Now, total number of students = (x + 8) Sum of x students + sum of 8 students = sum of total (x + 8) students ⇒ 58.5x + 516 = (x + 8)59.46 ⇒ 58.5x + 516 = 59.46x + 475.68 ⇒ 59.46x - 58.5x = 516 - 475.68 ⇒ 0.96x = 40.32 ⇒ x = 40.32/0.96 ⇒ x = 42 ∴ The number of students initially in a class is 42.