Out With The Old, In With The New

Algebra Level 1

The average age of the members of a 10-person committee is the same as it was 4 years ago, because an old member has just been replaced by a new member.

How much younger is the new member than the old member who was replaced?


The answer is 40.

Samyak Jain by samyak jain , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Samyak Jain
Jan 18, 2016

Let the sum of nine member (total) =x and the age of old one=z so its average 4 yrs before=(x+z)/10. after 4 yrs let z be replaced by y. so now avg=(x+4*10+y)/10

now (x+z)/10=(x+40+y)/10 so after solving it found z=y+40. so old person is 40yrs older than young one.

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I have a question, why isn't it (x+z)/10=(x+36+y)/10 because after 4 years, it must be (z+4) replaced by y.

Minh Mẫn Bùi - 5 years, 4 months ago

Log in to reply

While this is true in this case your looking for the difference (z+4)-y which is still 40

Jerry McKenzie - 4 years, 6 months ago

Consider it this way.... (At Present)Let the sum of 9 members age= x and the new member = y. So average is (x+y)/10. (4 years ago) the sum of nine members age = x-36 and the old member age was= z-4. So avg =( x+z-40)/10. Therefore, (x+y)=(x+z-40) So y=z+40 Note: y and z are the present ages.

Ashutosh Kapre - 4 years ago

Log in to reply

Edit: y=z-40.

Ashutosh Kapre - 4 years ago

I agree with you!

kattos kattos - 5 years, 4 months ago

I think the answer should be 36. Four years ago, let the sum of the nine who stayed be x, and the old member be z, so the average then was (x + z)/10. Now the present board consists of nine members of age x + 36 and a new member of age u, so the average is (x + 36 + u)10. Equating the two averages, (times 10), x + z = x + 36 +u, so z - u = 36. Ed Gray

Edwin Gray - 3 years, 6 months ago

Log in to reply

The answer is 40, after 4 years, z should +4.

Thiam Yu Siew - 1 year, 5 months ago

The answer should be 36.

A Former Brilliant Member - 1 year, 6 months ago

The answer should be 36

A Former Brilliant Member - 1 year, 5 months ago
Jaime Puente
Mar 16, 2019

Non-math explanation:

Every year that passes, all the members are 1 year older, so the sum of all the ages would be 10 higher. Then in 4 years, the sum of ages would be 10*4=40 years higher.

Then if both 4 years ago average and the current average are the same, then the difference between the replaced member and the new member has to be 40 years less.

0 Helpful 1 Interesting 0 Brilliant 0 Confused

Only 9 of the members are 4 years older. The oldest is removed from the new average. The new younger member is X. (X1+X2+X3+X4+X5+X6+X7+X8+X9+X10) - (X1+X2+X3+X4+X5+X6+X7+X8+X9) -9*4 = X, thus, X10=X+36.

A Former Brilliant Member - 1 year, 6 months ago

Log in to reply

Exactly what I got.

Kano Boom - 8 months ago

Let S be the sum of ages of all old members and let a and b be the old member who was replaced and the new member who was added respectively. We have (S-40)/10=(s-a+b)/10. Simplifying gives s-40=s-a+b, s cancels andwe rearrange to get a-b=40.

Mr. Krabs - 2 months, 1 week ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...