Aptitude - Average - Discussion

5. 

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

[A]. 76 kg
[B]. 76.5 kg
[C]. 85 kg
[D]. Data inadequate
[E]. None of these

Answer: Option C

Explanation:

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

Weight of new person = (65 + 20) kg = 85 kg.

Video Explanation: https://youtu.be/ceg2jvHsiJU


Mariam said: (Jul 18, 2010)  
65 is the weight of only 1 of the 8 persons. Then how can you take it as d weight of all d persons?

Anonymous said: (Oct 27, 2010)  
@ Mariam: Let x be the average weight
First case: Sum of weights of people / 8 people = x
So the sum of weights of people = 8x
Second case: Sum of weights of people / 8 people = x + 2.5
So the sum of weights of people here is 8(x + 2.5) = 8x + 20

So the difference between both sums is essentially the new heavier person that was added which is:
8x + 20 - 8x = 20
So the new guy weights 20kg more than the old guy.
So new guy weights: 65 + 20 = 85kg

Riya said: (Nov 8, 2010)  
Thank you. I was confused earlier. Your explanation has cleared it all. :).

Aparna said: (Dec 29, 2010)  
Oral method:.

When the replaced persons weight was 65 kg then no effect takes place.

But due to him all of thems weight has been increased by 2.5kg.

So,

8*2.5=20.

65+20=85.

Vinoth M said: (Feb 17, 2011)  
When a new person weight is added to 8 peoples weight each person weight is increased by 2.5%

Then weight increased is 8*2.5=20
So the new person age is 65+20=85

Aamir said: (Jul 24, 2011)  
A new person's weight is 65 kg and why add early 8 person, where as he is a replaced person.

Tinku said: (Aug 5, 2011)  
@Aamir

It is not weight of the new person. It is weight of which person who is replace from the new person.

Let weight of new person is = x.

Replace person weight=65kg.

Total person=8.

Let total weight 8 person is W.

Before replace of a person.

W/8=a.

Here the a is the average.

Now replace a person which weight is 65kg.

(x+W-65)/8=a+2.5.

Put w=8a from above eqn.

Wet get x=85kg.

Bhanu said: (Aug 12, 2011)  
Hai Friends.

Try this method.

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 "85".

Isha said: (Aug 20, 2011)  
Thanks bhanu your method is so good.

Kumar said: (Aug 25, 2011)  
Here we are replacing the person of 65kg, then how 2. 5kg will effect to replaced person.

Jagat said: (Oct 8, 2011)  
Thank for this simplication.

Shiya said: (Nov 15, 2011)  
@kumar

Hi kumar in the problem they are saying that it wil be effect 2.5 kg that means may be new person weight will be greater than other remaining 7 persons. In this situation they may be effect rite.

Radhika said: (Nov 23, 2011)  
Average of quantities is 22 and average of 36 quantities is 25. What is the average of all the 50 quantities?

Muthu said: (Nov 24, 2011)  
@Banu nice method.

Chithramol Er said: (Dec 20, 2011)  
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

Ankit Saxena said: (Feb 25, 2012)  
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

Rahul said: (Nov 9, 2012)  
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.

Karthik said: (May 9, 2013)  
(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.

Sandeepkumar said: (Jul 9, 2013)  
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.

Amar Sahoo said: (Aug 20, 2013)  
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.

Rahul said: (Aug 25, 2013)  
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.

Swetha said: (Sep 11, 2013)  
Why do you add 20 for calculating the weight of new person? how is that logic?

Virat said: (Jan 8, 2014)  
@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.

Ganesh Raw said: (Jun 22, 2014)  
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.

Manoj Kumar said: (Nov 25, 2014)  
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.

Jay said: (Dec 8, 2014)  
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.

Mukesh said: (Feb 3, 2015)  
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.

Vineela Reddy said: (Feb 7, 2015)  
@Manoj kumar is it useful for all?

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

Hemanth said: (Feb 25, 2015)  
Weight of newly came person is = Weight of replaced person + (no of persons*increased in weight).

=>65+ (8*2.5).

=>65+20.

=>85.

B.E(Bekar Engg) said: (Mar 4, 2015)  
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;

Sarvesg said: (May 2, 2015)  
The first line says average weight weight of person is increased by 2.5.

1) So the total weight increase is = 2.5*8 = 20.

2) Then it says when old person weighting 65 kg is replaced by new one since the weight increase is because of only one person add the old person weight+the average weight = 65+20 = 85.

Fakhar said: (Jun 21, 2015)  
I am totally confused. Can any one give me solution?

Sneha said: (Jul 11, 2015)  
@Manoj Kumar Sir, your tricks are really useful.

Manoj Kumar said: (Jul 19, 2015)  
Thanks for your support guys. Will post more useful information in future.

Saravanan said: (Aug 22, 2015)  
Replaced value+(Increase in average*Total number of observation).

Mahnoor said: (Sep 17, 2015)  
I'm totally confused. Why method change again an again?

Victor said: (Dec 5, 2015)  
Can I have some more tricks?

Honey said: (Dec 10, 2015)  
But one person is excluded from 8 and a new person comes?

Nandini said: (Dec 24, 2015)  
Hai friends.

Can any one explain me why we add 20+65? Why not 20-65?

Naveen said: (Feb 10, 2016)  
The average of marks obtained in 120 students was 35. If the average of passed candidates was 39 and that of failed candidates is 15, the no of candidates who passed the examination is?

Anil Kumar Basam said: (Apr 11, 2016)  
Total 9 person's average weight = 65 -> So, 65*9 = 585.
Every person comes in the place increases 2.5 -> So, 65 - 2.5 = 62.5.
8 persons average weight = 62.5.

Sum of the elements = average*total numberof elements.
=> 62.5*8 =500.

Sum of 9 persons - sum of 8 persons = 585 - 500= 85.
New person weight = 85kg.

Sagar said: (May 4, 2016)  
Is there any shortcut method to solve this problem? Please help me.

S S Kumar said: (May 5, 2016)  
@NANDINI.

We are adding 20 to 65 because the average weight of 8 persons is being increased to 2.5 kg, by the new person who has been replaced by the existing one.

This directly implies that the new person who added into these will weigh more than the replaced one.

Hope you understand this.

Priyanka Verma said: (Jul 6, 2016)  
Let average = x.
Then, sum = 8x.

Now after replacement:

8x - 65 + y = 8 (x + 2.5),
8x - 65 + y = 8x + 20.
y = 65 + 20.
y = 85.

Saisangeetha said: (Aug 2, 2016)  
@Bhanu.

Your explanation is good.

Rasiga said: (Sep 20, 2016)  
There is very simple formula for this.

Weight of New person = No of Persons * Increased weight + Replaced.

So, 8 * 2.5 + 65 = 85.

M Rajoo said: (Oct 4, 2016)  
Thank you @All, for the explanation.

Koteswararao Chimmili said: (Dec 15, 2016)  
The average weight of 8 person's increases by 2.5 kg.

Assume 8 persons.
a, b, c, d, e, f , g, h then,

(a + b + c + d + e + f + g + h)/8 = x + 2.5
(a + b + c + d + e + f + g + h = 8 ( x + 2.5)
= 8x + 20 -----------> 1

When a new person comes in place of one of them weighing 65 kg
then

(a + b + c + d + e + f + g + h + 65)/9 = x
(a + b + c + d + e + f + g + h + 65) = 9 x
(a + b + c + d + e + f + g + h= 9x - 65 -------------> 2

Solving eguation1 and 2

8x + 20 = 9x - 65.
20 + 65 = 9x - 8x.
85 = x.

Chitti said: (Jan 4, 2017)  
The average age of a group of 12 persons is 40 years. If one more person is included then average increases by 1. What is the age of new person?

Anis said: (Feb 1, 2017)  
@Chitti.

Answer : 53 years.

(Sum of age of 12 people)/12= 40 [given].
Thus, Sum of age of 12 people= 480 years.

Let 'x' be the age of the new person.
(Sum of age of 12 people + x)/13 = 41 [given, average increases by 1].
Sum of age of 12 people + x = 533.
480 + x= 533.
x= 53.

Abhishek said: (Apr 20, 2017)  
@Chitti.

Now, pepole is 13.
Avg. inc by 1.
Therefor 40 + 1><13 = 53.

Riddhi said: (Jun 29, 2017)  
It's said in question that avg increase by 2.5,
So we can say orginal average maybe X.

X+ 2.5 is avg of 8 people when a new person added instead of a man having 65 kg.
So Wat I meant is deviation is 2.5 or difference 2.5 ( avg b4 a new person was not added )---(Avg after a new person got added).

2.5*8 = 20 kg is the weight that is needed to be disturbed amongst 5 people to get avg of 2.5 so,
20+65 = 85kg.

Marshall said: (Jul 1, 2017)  
The mean mass of 5 men is 78kg, the mass of four of them are 74kg, 76kg, 77kg and 86kg, please what is the mass of the fifth?

Lakshmi said: (Jul 7, 2017)  
The average age of the mother and her six children is 12 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?

Please explain it with the answer.

Abhishek said: (Jul 11, 2017)  
@Marshall.

The mass of 5th person is 77kg.

Abhi said: (Jul 17, 2017)  
Can we simply take 2.5*8 which 20 and add 20 to 65 which is 85?

Likha Kamin said: (Jul 21, 2017)  
I can't understand, according to question sum of all person's is 65 kg and one person is just replaced then in such case we should substract from total weight.


Anyone please clear my confusion.

Roshni Shaji said: (Jul 22, 2017)  
In the first case,

Let, X be the average weight of 8 persons
W1 be total weight of 8 persons
7sw be the total weight of 7 persons excluding 65 year old person
W1 = 7sw + 65
we have W1/8=X ==> (7sw+65)/8 = X
7sw+65 = 8 X
7sw = 8 X - 65 --------> equation no.(1)

In the second case,
Let, W2 be the total weight of 8 persons including the newcomer
Now be the weight of new comer
We get W2 = 7sw + Nw --------> (2)
We have W2/8 =X+2.5
W2 = (X+2.5)*8
W2 = 8X +20
Therefore (2) becomes
7sw+Nw = 8X + 20 --------> (3)

Substitute (1) in (3)
We get, 8X - 65 +Nw = 8X + 20.
ie: Nw = 8X + 20 - 8X +65,
Nw = 20+65.
= 85,
ie, the weight of the person who joined in place of the person weighing 65 kg is 85 kg.

Roshni Shaji said: (Jul 22, 2017)  
The average age of the mother and her six children is 12.
ie. (sum of ages of 6 children + Age of mother)/7 = 12.
ie Sum of ages of 6 children + age of mother = 12*7 = 84.
Age of mother = 84 - sum of ages of 6 children ----> 1.

The average is reduced by 5 yrs when the age of mother is excluded
ie.the average age of 6 children = 12 -5.
ie the sum of ages of children / 6 = 7.
sum of ages of children = 6*7 =42.
Sum of ages of children = 42.

Substitute this sum in (1) we get,
Age of mother = 84 - 42.
Age of mother = 42 years (Answer).

Roshni Shaji said: (Jul 22, 2017)  
Hai @Likha,

The question is very clear. it says. a person of 65 kg left and a new comer joined.
Average = (total sum of the scores) divided by No. of scores.
Sum of all persons (including 65 kg weighing person)/8 = X(average).
Sum of weight of 7 persons = 8X - 65 ------------------(1)
When joined another who weighs N, average increased by 2.5 kg
ie (sum of 7 person's weight + N) / 8 = X +2.5,
From (1) we get (8X - 65 + N) / 8 = X + 2.5,
8X - 65 + N = 8 *(X+ 2.5),
8X - 65 + N = 8X + 20,
N = 8X + 20 - 8X + 65,
N = 20 + 65,
N = 85.

The weight of new comer is 85 kg. the answer

Roshni Shaji said: (Jul 22, 2017)  
@Naveen.

Total number of students = 120,
Let X be the number of passed candidates then 120-X is the number of failed candidates.
Average marks of 120 students = 35,
Average of passed candidates =39,
Average of failed candidates =15,

Therefore,
Total marks of 120 students = 35*120 = 4200,
Total marks of passed candidates= 39 * X,
Total marks of failed candidates = 15 *(120 - X) = 1800 -15 X,
Total marks of passed candidates + Total marks of failed candidates = Total marks of 120 sudents.

ie 39X + 1800 - 15X = 4200,
39X - 15X = 4200 - 1800,
24X = 2400,
X = 100,
ie The number of passed candidtes = 100 (Answer).

Niraj Shrestha said: (Sep 8, 2017)  
The average of six consecutive integers in increasing order size is 9.5. What is the average of the last three numbers?

Can anyone solve this?

Elvis Fernandes said: (Feb 26, 2018)  
@Niraj.

The answer is 46.

Anand said: (Feb 27, 2018)  
The average weight of three men 'X', 'Y' and 'Z' is 75 kgs. Another man 'A' joins
the group and the average weight now becomes 80 kgs. If another person 'B' whose
weight is 5 kgs more than 'A' replaces 'X', then the average weight of 'Y', 'Z', 'A' and
'B' will be 85 kgs. What is the weight of 'X'?

Can anyone solve this?

Pritha said: (May 28, 2018)  
Thanks @Bhanu.

Jeevitha said: (Jul 3, 2018)  
Your method is good, Thanks @Bhanu.

Manisha said: (Sep 6, 2018)  
Thanks @Anonymous.

Hilal Ahmad Bhat said: (Dec 1, 2018)  
Let the average weight of 8 persons be x and the weight of first 7 persons be A.

The weight of 8 persons is A+ 65 = 8x ---> (1)
After replacing the person having weight 65, the average weight of 8 persons increased by 2.5
Now the average weight of 8 persons will be 8(x+2.5) and;

The weight of 8 persons will be A + Z(replaced person weighing 65) = 8(x+2.5) ---> (2)
Subtract (1) from (2) i.e.,
A+Z-(A+65) = 8(x+2.5) - 8x,
A+Z-A-65 = 8x + 20 -8x,
Z-65 = 20,
Z = 20+65,
Z = 85 Weight of replaced person.

Naveen Kumar K said: (Dec 8, 2018)  
Thanks for the answer. @Bhanu.

Fahad Riaz said: (Feb 10, 2019)  
Total weight of 8 persons is 520 (65*8).
Now, a total weight of 7 persons is 455 (520-65),
Now try every option to get 2.5% increase,
(455+85)/8 is equal to 67.5,
The total increase is 2.5 KG (67.5-65),
Ans is 85 KG.

Saravanan said: (Jul 23, 2019)  
Let x be an average of 8 persons.
Let y be the weight of the new person.
(x+y-65)/8 = (x/8)+2.5,
x+y-65 = x+20,
y-65 = 20,
y = 85.

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