Question
- The average age of a board of 8 trustees remains the same as it was 3 years ago, when one of them is replaced by a new member. The new member is younger than the trustee in whose place he has been replaced by
Answer: Option B
Let the average age of the board of 8 trustees be x.
Then, the sum of the ages of the 8 trustees would be 8x.
Three years ago, the sum of their ages would have been (8x - 8*3) = (8x - 24).
Let the age of the trustee who has been replaced be y, and the age of the new member be z.
We know that z < y, since the new member is younger than the trustee he has replaced.
After the replacement, the sum of the ages of the 8 trustees remains the same as it was 3 years ago. Therefore, we have:
(8x - y + z) = (8x - 24)
Simplifying this expression, we get:
z - y = -24
Since z < y, we can rewrite this as:
y - z = 24
This means that the difference in ages between the trustee who has been replaced and the new member is 24 years.
Therefore, the answer is option B, 24 years.
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Let the average age of the board of 8 trustees be x.
Then, the sum of the ages of the 8 trustees would be 8x.
Three years ago, the sum of their ages would have been (8x - 8*3) = (8x - 24).
Let the age of the trustee who has been replaced be y, and the age of the new member be z.
We know that z < y, since the new member is younger than the trustee he has replaced.
After the replacement, the sum of the ages of the 8 trustees remains the same as it was 3 years ago. Therefore, we have:
(8x - y + z) = (8x - 24)
Simplifying this expression, we get:
z - y = -24
Since z < y, we can rewrite this as:
y - z = 24
This means that the difference in ages between the trustee who has been replaced and the new member is 24 years.
Therefore, the answer is option B, 24 years.
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Now since the average age of the current trustees and the previous trustees is same,
(x + y)/8=(x + z + 24)/8
The 24 value accounts for the time lapse of 3 years for each of the 8 trustees.
Thus we get y - z = 24
Therefore the age gap is 24
Now
x+y/8 = x+z+24
Here 24 is the total age of 8 trustees in 3 yrs
So y-z = 24
8x3=24