Question

The average age 9 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?​

Answer 1

Answer:

Let the sum of eight members =x and the age of old one=z so its average 2 yrs before=(x+z)/9. after 2 yrs let z be replaced by y. so now avg=(x+2*9+y)/9

now (x+z)/9=(x+18+y)/9 so after solving it found z=y+18 so old person is 18 yrs older than young one.

Answer 2

The younger member is 18 years younger than the old member.

Given:

The average age of 9 members of a committee is the same as it was 2 years ago because an old number has been replaced by a younger member.

To Find:

How much younger the new member is than the old member.

Solution:

Two years ago the committee consisted of 9 members. Among them, let us assume that the sum of ages of 8 other members is 'x' and the age of the ninth member who eventually gets replaced is 'y'.

Hence, average of the ages of committee members before 2 years = $(\frac{x+y}{9} )$

After 2 years, the old member gets replaced by a younger member.

Let the age of the new member be 'z'

So the current average of the ages of the committee members = $(\frac{x+(2*9) + z}{9} )$

From our given condition, the average of the ages of committee members before 2 years = the current average of the ages of the committee members.

⇒ $(\frac{x+y}{9} )$= $(\frac{x+(2*9) + z}{9} )$

⇒ y = 18 + z

⇒The younger member is 18 years younger than the old member.

Therefore, the younger member is 18 years younger than the old member.

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