Aptitude - Average - Discussion

@Chitti.

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

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.

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?

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.

@Marshall.

The mass of 5th person is 77kg.

Can we simply take 2.5*8 which 20 and add 20 to 65 which is 85?

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.

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.

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).

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