Question
The average age of a group of eight children is 9 years.
Two children, whose ages were 7 years more and 5 years more than the average age, left. Two new children, whose average age is 4 years more than the given average age, join the group. Find the new average age.Solution
Initial sum of the ages of 8 children = 9 x 8 = 72 years Ages of the children leaving: 9 + 7 = 16 years and 9 + 5 = 14 years, Sum of the ages of children leaving = 16 + 14 = 30 years Sum of the ages after two children left = 72 - 30 = 42 years Sum of the ages of 2 new children = (9 + 4) x 2 = 26 years Total sum of the ages with new children = 42 + 26 = 68 years Number of children now= 8 - 2 + 2 = 8 New average age = 68/8 = 8.5 years
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