Aptitude - Average - Discussion

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.

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?

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.

@Chitti.

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

@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.

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?

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.

Thank you @All, for the explanation.

There is very simple formula for this.

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

So, 8 * 2.5 + 65 = 85.

@Bhanu.

Your explanation is good.