Question
Download Solution PDFThe average age of a group of friends is 27 years. If 4 new friends whose average age is 25 years join them, the average age of the entire group becomes 26 years. How many people were there in the group initially?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The average age of a group of friends is 27 years.
If 4 new friends whose average age is 25 years join them, the average age of the entire group becomes 26 years.
Calculation:-
Let's denote the initial number of friends in the group as "N".
The sum of the ages of the initial N friends = 27N.
After 4 new friends join the group, the average age becomes 26 years.
Now, the total sum of ages of the entire group after the 4 new friends join,
⇒ 26 (N + 4).
According to this question,
⇒ 27N + 4 × 25 = 26N + 104
⇒ 27N + 100 = 26N + 104
⇒ N + 100 = 104
Subtract 100 from both sides: N = 4
∴ Initially, there were 4 friends in the group.
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