Aptitude - Average - Discussion

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 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.

@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).

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

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).

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.

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.

Age of captain = 26 ...
So the age of the wicket-keeper who is 3 years older than the captain = 29
Let avg of 11 members be x, then
The sum of observations /11 = x.

I. e 26+29+ remaining sum of 9 members = 11x.
Remaining sum of 9 = 11x-55--->(1)
Given that, avg of the remaining 9 will be one less than the total average.
So total avg is x, then the of 9 is x-1.

I. e sum of remaining 9/9 = x-1.
Sum of remaining 9 = 9x-9 ----> (2)
9x-9 = 11x-55 from 1 and 2.

11x -9x = -9+55.
2x = 46,
x= 46/2 = 23.

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.

@ 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