Aptitude - Average - Discussion

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?

@Niraj.

The answer is 46.

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?

@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).

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.

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.

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

@Marshall.

The mass of 5th person is 77kg.