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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 age of the replaced member and new member?
- a)2 years
- b)8 years
- c)15 years
- d)25 years
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
After replacing an old member by a new member, it was found that the a...
Age decreased = (5 × 3) years = 15 years
So, the required difference = 15 years
Most Upvoted Answer
After replacing an old member by a new member, it was found that the a...
Let's assume the ages of the five members of the club before the replacement are A, B, C, D, and E. After the replacement, the ages of the new members are A, B, C, D, and F.
Let's calculate the average age of the members before the replacement. We know that the average is the sum of the ages divided by the number of members.
Average age before replacement = (A + B + C + D + E)/5
Now, let's calculate the average age of the members after the replacement, which is the same as it was 3 years ago. Since the average age hasn't changed, it means that the sum of the ages of the members after the replacement is the same as it was 3 years ago.
Average age after replacement = (A + B + C + D + F)/5
Since the average age hasn't changed, we can equate the two equations:
(A + B + C + D + E)/5 = (A + B + C + D + F)/5
Simplifying the equation:
A + B + C + D + E = A + B + C + D + F
The terms A, B, C, and D cancel out from both sides of the equation:
E = F
This means that the age of the replaced member (E) is equal to the age of the new member (F). Therefore, the difference between their ages is zero.
However, the given options do not include zero as a possible answer. This suggests that there might be a mistake in the question or options provided. Without any additional information, it is not possible to determine the correct answer.
Let's calculate the average age of the members before the replacement. We know that the average is the sum of the ages divided by the number of members.
Average age before replacement = (A + B + C + D + E)/5
Now, let's calculate the average age of the members after the replacement, which is the same as it was 3 years ago. Since the average age hasn't changed, it means that the sum of the ages of the members after the replacement is the same as it was 3 years ago.
Average age after replacement = (A + B + C + D + F)/5
Since the average age hasn't changed, we can equate the two equations:
(A + B + C + D + E)/5 = (A + B + C + D + F)/5
Simplifying the equation:
A + B + C + D + E = A + B + C + D + F
The terms A, B, C, and D cancel out from both sides of the equation:
E = F
This means that the age of the replaced member (E) is equal to the age of the new member (F). Therefore, the difference between their ages is zero.
However, the given options do not include zero as a possible answer. This suggests that there might be a mistake in the question or options provided. Without any additional information, it is not possible to determine the correct answer.
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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 age of the replaced member and new member?a)2 yearsb)8 yearsc)15 yearsd)25 yearsCorrect answer is option 'C'. Can you explain this answer?
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