Aptitude - Average - Discussion

It is not given in question that average weight of each was 65 kg instead it was the weight of only that person who was replaced so they have assumed and done wrongly.

Why do you add 20 for calculating the weight of new person? how is that logic?

@Sweta weight of 8 persons is increasing when a new person is coming by replacing a person whose weight is given 65 kg,

Now to know the weight of new person we have add the increased weight in 65 kg simple.

8*2.5 = 20 kgs.

So now the weight of new person is 65+20 kg = 85kg.

Guys it's simple.

Let consider the first case:

The average weight of 8 people be x.
So,
(a+b+c+d+e+f+g+65)/8=x : ( one of the person weighs 65)
=>a+b+c+d+e+f+g+65=8x .........(1).

If the person who weighs 65kg was replaced the average.
i.e. Let the new person weight be Z.

=>(a+b+c+d+e+f+g+Z)/8= x+2.5. :( the average increased by 2.5).
=> (a+b+c+d+e+f+g+Z)=8x+20 ..........(2).

From (1) =>. a+b+c+d+e+f+g+8x= -65 ..........(3).
From(2) =>. a+b+c+d+e+f+g+8x= -z + 20.........(4).

Compare (3) & (4).

-Z+20= -65.
Z= 85 kg.

Is the answer.

Dear Friends.

Try this one below. There are only the following three cases possible if a group is disturbed.

Case 1: If a person is replaced by another one (Note: Here number of persons in the group remains same after replacement).

Case 2: If a person joins the existing group (Note: Here number of persons in the group will get increased by 1 after joining of a new one).

Case 3: If a person leaves from existing group (Note: Here number of persons in the group will get decreased by 1 after removal of old one).

Formula for Case 1:

1. If average weight is increased, then.

Weight of new comer = Weight of the person left + (No. of persons X Increase in average weight).

2. If average weight is decreased then.

Weight of new comer = Weight of the person left - (No. of persons X Decrease in average weight).

Formula for Case 2:

1. If average weight is increased then.

Weight of new comer = Previous average weight + (No. of persons including new comer X Increase in average weight).

2. If average weight is decreased then.

Weight of new comer = Previous average weight - (No. of persons including new comer X Decrease in average weight).

Formula for Case 3:

1. If average weight is increased then.

Weight of person left = Previous average weight + (No. of persons excluding the person left X Increase in average weight).

2. If average weight is decreased then.

Weight of person left = Previous average weight - (No. of persons excluding the person left X Decrease in average weight).

The above formulas can also be used for calculating age instead of weight & can be used for other things instead of persons.

Hope this was useful.

In this case problems you people just recall this formula:

N - R = (+ or -)nx.

N - new items added.
R - removed items.
n - average of the sum.
x - decrease or increase.

Put + when increase.
- for decrease.

Now see:
N - 65 = + 8(2.5).
N = 85.

Old School method.

Let Z+65 be weight of 8 person and their average be A.

So, (z+65)/8 = A .......(i).

Now with the replacing the person with 65 KG weight with new person, average becomes A+2.5, let the weight of new person be x KG.

So, (Z+x/8) = A+2.5 .......(ii).

Subtraction (i) from (ii).

(x+65)/8 = 2.5.

Therefor, x = 85.

@Manoj kumar is it useful for all?

Please give the clear information I'm ok but little confused.

Weight of newly came person is = Weight of replaced person + (no of persons*increased in weight).

=>65+ (8*2.5).

=>65+20.

=>85.

Let average of 8 person weight = x;

x/8 = 2.5;
x = 8*2.5.
x = 20;

New person is add with weight = 65.

65+20 = 85.
Ans = 85;