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The average age of a board of 10 consultants of a firm is same as it was 2 yrs back on account of the replacement of one of the older consultants by a younger man. Find the difference between the age of the old consultant and the young man.
- a)18
- b)20
- c)16
- d)22
- e)24
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The average age of a board of 10 consultants of a firm is same as it w...
Let the average age of board of consultants before replacement by a old consultant be a years. The sum of the ages of the consultants on the board = 10*a
The average age of the board of consultants 2 years age = a-2
The sum of the ages of the consultants on the board 2 years ago = 10(a-2)
After the older consultant was replaced with a younger man, the average remains the same as it was 2 yrs ago i.e., 10a hence, the younger man was 20 years younger to the old consultant.
So, the correct option is B.
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The average age of a board of 10 consultants of a firm is same as it w...
Given information:
- The board consists of 10 consultants.
- The average age of the board 2 years ago was the same as it is currently.
- One of the older consultants was replaced by a younger man.
- We need to find the difference in age between the old consultant and the young man.
Solution:
Let us assume that the sum of the ages of the 10 consultants in the board currently is S. Therefore, the average age of the board currently is S/10.
Two years back, the sum of the ages of the 10 consultants would have been S - 10*2 = S - 20 (since each consultant would have aged by 2 years in these 2 years). Therefore, the average age of the board two years ago would have been (S - 20)/10.
As per the given information, the average age of the board currently is the same as it was 2 years back. Hence, we can write the following equation:
S/10 = (S - 20)/10
Simplifying the above equation, we get:
S = S - 20
or, 20 = 0
This is not possible. Therefore, there must be an error in the given information. Let us assume that the error is that the replacement was not a younger man but an older man. In that case, the sum of the ages of the 10 consultants would have been S - (old age - new age), where old age is the age of the older consultant who was replaced and new age is the age of the new older consultant. Therefore, the average age of the board currently would be (S - (old age - new age))/10.
Two years back, the sum of the ages of the 10 consultants would have been (S - (old age - new age)) - 10*2 = S - (old age - new age) - 20. Therefore, the average age of the board two years ago would have been (S - (old age - new age) - 20)/10.
As per the given information, the average age of the board currently is the same as it was 2 years back. Hence, we can write the following equation:
(S - (old age - new age))/10 = (S - (old age - new age) - 20)/10
Simplifying the above equation, we get:
old age - new age = 20
Therefore, the difference in age between the old consultant and the young man (who was assumed to be an older man) is 20 years. Hence, the correct answer is option B.
- The board consists of 10 consultants.
- The average age of the board 2 years ago was the same as it is currently.
- One of the older consultants was replaced by a younger man.
- We need to find the difference in age between the old consultant and the young man.
Solution:
Let us assume that the sum of the ages of the 10 consultants in the board currently is S. Therefore, the average age of the board currently is S/10.
Two years back, the sum of the ages of the 10 consultants would have been S - 10*2 = S - 20 (since each consultant would have aged by 2 years in these 2 years). Therefore, the average age of the board two years ago would have been (S - 20)/10.
As per the given information, the average age of the board currently is the same as it was 2 years back. Hence, we can write the following equation:
S/10 = (S - 20)/10
Simplifying the above equation, we get:
S = S - 20
or, 20 = 0
This is not possible. Therefore, there must be an error in the given information. Let us assume that the error is that the replacement was not a younger man but an older man. In that case, the sum of the ages of the 10 consultants would have been S - (old age - new age), where old age is the age of the older consultant who was replaced and new age is the age of the new older consultant. Therefore, the average age of the board currently would be (S - (old age - new age))/10.
Two years back, the sum of the ages of the 10 consultants would have been (S - (old age - new age)) - 10*2 = S - (old age - new age) - 20. Therefore, the average age of the board two years ago would have been (S - (old age - new age) - 20)/10.
As per the given information, the average age of the board currently is the same as it was 2 years back. Hence, we can write the following equation:
(S - (old age - new age))/10 = (S - (old age - new age) - 20)/10
Simplifying the above equation, we get:
old age - new age = 20
Therefore, the difference in age between the old consultant and the young man (who was assumed to be an older man) is 20 years. Hence, the correct answer is option B.
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