Aptitude - Average - Discussion

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.

@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.

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

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.

Let us take 'x' be the new person.

'x' replaces the person having 65 kg weight i.e. x-65.

Total weight increased = (8 x 2.5) kg = 20 kg.

So we can put it in an equation i.e.

x - 65 = 20.

x = 20 + 65.

x = 85 ANS.

Let x be the average weight,

Total weight incremented is = x+ 2.5.
Then,

avg.
7x-65 = 8(x+2.5).

7x-65 = 8x+20.

Then x = 85.

(w1+w2+w3+...+w8)/8 = x kg - eq1.

Let w2 be the person who has been replaced.

Let it be denoted by w2n.

So now,

(w1+w2n+w3+....+w8)/8 = x+2.5 - eq2.

Replacing x in eq2 with x from eq1 we get,

w2n-w2 = 20.

=> w2n = 85.

Avg = x.

Sum of 8 person's weight/8 = x.

Sum of 8 person's weight= 8x.

Sum of 8 person's weight = 8x+20.

8x+20-8x-20=0.

8x+20-8x = 20.

Therefore 20+65=85.

Remember the formula for this type of
new person weight=weight of person tht left+total men*average increased after entry of new men...
Hope it wil help u all

New person weight =Replaced person weight+ (no. Of persons*increased weight).

Replaced person weight =65.

No. Of persons =8.

Increased weight =2.5.

These all values are replaced in the formula, then we get the answer as 85