The average weight of 20 students in a group is 54 kg. If 12 students of average weight 52 kg join the group and 7 students of average weight 56 kg leave the group, then what will be the average weight (in kg) of the remaining students in the group?

Explanation

Given:Average weight of 20 students = 54 kg Average weight of 12 students = 52 kg Average weight of 7 students = 56 kg Formula used:Average = (Sum of all weight)/(Total no. of weight) Calculation:According to question⇒ (Sum of 20 students)/20 = 54 ⇒ Sum of 20 students = 54 × 20 ⇒ Sum of 20 students = 1080 ∴ Sum of 12 students = 52 × 12 ⇒ Sum of 12 students = 624 ⇒ Sum of 7 students = 56 × 7 ⇒ Sum of 7 students = 392 Average of remaining students = (Sum of 20 students + Sum of 12 students - Sum of 7 students)/(20 + 12 - 7) Average of remaining students = (1080 + 624 - 392)/25 Average of remaining students = 1312/25 = 52.48 ∴ Average of remaining students is 52.48.