Question
A class of 45 students has a total weight of 1080 kg.
Two students with weights 22 kg and ‘z’ kg leave the class, and a new student with weight (3z + 12) kg joins. The average weight of the class rises by 1 kg. What is the weight of the new student?Solution
ATQ,
Initial average = 1080 / 45 = 24 kg Final average = 24 + 1 = 25 kg Final number of students = 45 – 2 + 1 = 44 Final total weight = 25 × 44 = 1100 kg According to the question, 1080 – 22 – z + (3z + 12) = 1100 ⇒ 1058 + 2z + 12 = 1100 ⇒ 1070 + 2z = 1100 ⇒ 2z = 1100 – 1070 = 30 ⇒ z = 30 / 2 = 15 Weight of new student = 3z + 12 = 3 × 15 + 12 = 45 + 12 = 57 kg
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