Question
The average age of a group of nine children is 7 years.
From the group, three children, whose ages were 3 years more, 2 years more, and 4 years more than the average age, left. Six new children, whose average age is 2 years more than the given average age, join the group. Find the new average age.Solution
Initial sum of the ages of 9 children = 7 x 9 = 63 years Ages of the children leaving: 7 + 3 = 10 years, 7 + 2 = 9 years, and 7 + 4 = 11 years, Sum of the ages of the children leaving the group = 10 + 9 + 11 = 30 years Sum of the ages after three children left = 63 – 30 = 33 years Sum of the ages of 7 new children = (7 + 2) x 7 = 63 years Total sum of the ages with new children = 33 + 63 = 96 years Number of children now = 9 – 3 + 6 = 12 years New average age = 96/12 = 8 years
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