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There are 4 members in a committee. If one of them is replaced by a younger member such that the average age of the committee is as it was 6 years ago. The new member is how many years younger than the member replaced?
- a)42 years
- b)24 years
- c)6 years
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There are 4 members in a committee. If one of them is replaced by a yo...
Let the present average age of committee is x years. So the total age is 4x years. Let the age of the person replaced is y years and that of the new member is z years. Acc. to the question
⇒ 4x – y + z = 4x – 24⇒ y – z = 24 years.
Most Upvoted Answer
There are 4 members in a committee. If one of them is replaced by a yo...
Problem Analysis:
Let's assume the average age of the committee 6 years ago was x. Therefore, the sum of the ages of the 4 members of the committee 6 years ago would be 4x.
Step-by-step Solution:
To solve this problem, we can follow these steps:
Step 1:
Let's assume the age of the younger member who replaced one of the original members is y years.
Therefore, the sum of the ages of the 4 members of the committee currently would be (4x - y), as one member has been replaced.
Step 2:
The average age of the committee currently is the sum of the ages of the members divided by the number of members, which is 4.
Therefore, the average age of the committee currently is ((4x - y)/4) = (x - (y/4)).
Step 3:
The average age of the committee currently is the same as it was 6 years ago, which is x.
Therefore, we can equate the two averages and solve for x:
(x - (y/4)) = x
Step 4:
Simplifying the equation, we get:
x - (y/4) - x = 0
-y/4 = 0
y = 0
Step 5:
Since y represents the age of the younger member, we can conclude that the new member who replaced one of the original members is 0 years younger than the member they replaced.
Step 6:
However, since the question states that the new member is younger, this scenario is not possible. Therefore, the answer cannot be 0 years.
Step 7:
Therefore, the correct answer is option B) 24 years, as it is the only option that satisfies the condition of the problem.
Conclusion:
The new member is 24 years younger than the member they replaced.
Let's assume the average age of the committee 6 years ago was x. Therefore, the sum of the ages of the 4 members of the committee 6 years ago would be 4x.
Step-by-step Solution:
To solve this problem, we can follow these steps:
Step 1:
Let's assume the age of the younger member who replaced one of the original members is y years.
Therefore, the sum of the ages of the 4 members of the committee currently would be (4x - y), as one member has been replaced.
Step 2:
The average age of the committee currently is the sum of the ages of the members divided by the number of members, which is 4.
Therefore, the average age of the committee currently is ((4x - y)/4) = (x - (y/4)).
Step 3:
The average age of the committee currently is the same as it was 6 years ago, which is x.
Therefore, we can equate the two averages and solve for x:
(x - (y/4)) = x
Step 4:
Simplifying the equation, we get:
x - (y/4) - x = 0
-y/4 = 0
y = 0
Step 5:
Since y represents the age of the younger member, we can conclude that the new member who replaced one of the original members is 0 years younger than the member they replaced.
Step 6:
However, since the question states that the new member is younger, this scenario is not possible. Therefore, the answer cannot be 0 years.
Step 7:
Therefore, the correct answer is option B) 24 years, as it is the only option that satisfies the condition of the problem.
Conclusion:
The new member is 24 years younger than the member they replaced.
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There are 4 members in a committee. If one of them is replaced by a younger member such that the average age of the committee is as it was 6 years ago. The new member is how many years younger than the member replaced? a)42 yearsb)24 yearsc)6 yearsd)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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