Aptitude - Average - Discussion

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.

Is there any shortcut method to solve this problem? Please help me.

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We are adding 20 to 65 because the average weight of 8 persons is being increased to 2.5 kg, by the new person who has been replaced by the existing one.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

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.

@Bhanu.

Your explanation is good.

There is very simple formula for this.

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

So, 8 * 2.5 + 65 = 85.

Thank you @All, for the explanation.

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.

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?

@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.