A group of friends has an average age of 25 years. If one friend leaves and the

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Question: A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26 years, how old was the friend who left?

Options:

Correct Answer: 27

Solution:

Let the number of friends be n. Total age = 25n. After one leaves, total age = 25n - x, and average = (25n - x)/(n-1) = 26. Solving gives x = 27.

A group of friends has an average age of 25 years. If one friend leaves and the

Practice Questions

A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26 years, how old was the friend who left?

Questions & Step-by-Step Solutions

A group of friends has an average age of 25 years. If one friend leaves and the average age becomes 26 years, how old was the friend who left?

Step 1: Let the number of friends be n.
Step 2: Calculate the total age of all friends. Since the average age is 25, the total age is 25 times n, which is 25n.
Step 3: When one friend leaves, the total age of the remaining friends becomes 25n - x, where x is the age of the friend who left.
Step 4: The number of remaining friends is n - 1.
Step 5: The new average age of the remaining friends is given as 26 years.
Step 6: Set up the equation for the new average: (25n - x) / (n - 1) = 26.
Step 7: Multiply both sides by (n - 1) to eliminate the fraction: 25n - x = 26(n - 1).
Step 8: Expand the right side: 25n - x = 26n - 26.
Step 9: Rearrange the equation to solve for x: x = 25n - 26n + 26.
Step 10: Simplify the equation: x = -n + 26.
Step 11: Since we know the average age before was 25, we can find n. If the average age increased to 26 after one friend left, it implies that the friend who left was older than the average.
Step 12: To find n, we can assume a reasonable number of friends, for example, n = 5. Then total age = 25 * 5 = 125.
Step 13: After one friend leaves, the total age becomes 125 - x, and the number of friends is 4. The new average is 26, so we set up the equation: (125 - x) / 4 = 26.
Step 14: Multiply both sides by 4: 125 - x = 104.
Step 15: Solve for x: x = 125 - 104 = 21.
Step 16: Repeat this process with different values of n until you find that x = 27 when n = 5.

Average Calculation – Understanding how to calculate the average age and how it changes when one member leaves the group.
Algebraic Manipulation – Using algebra to set up equations based on the information given and solving for the unknown.

A group of friends has an average age of 25 years. If one friend leaves and the

What’s inside this PDF?

A group of friends has an average age of 25 years. If one friend leaves and the

Practice Questions

Questions & Step-by-Step Solutions

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