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Question

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

A
2 years
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B
4 years
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C
8 years
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D
15 years
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Solution

The correct option is D 15 years
Let the five members ages be x1,x2,x3,x4,x5
Let the one of the old member age be x1
Let the new member age be x6

Given that after replacing an old member by the new member, the average age of five members is the same as it was 3 years ago

Therefore, (x13)+(x23)+(x33)+(x43)+(x53)5=x2+x3+x4+x5+x65

x1+x2+x3+x4+x53(5)=x2+x3+x4+x5+x6

x115=x6

x1x6=15

Therefore the difference between the ages of the replaced and the new member is 15 years

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