Aptitude - Average - Discussion

Here;
2 +1/2 Means 5/2.
a = 65+8* 5/2.
a = 85 is the new person's weight.

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.

The new average is increased by 2.5, so we can say 8 * 2.5 = 20kg is the newly increased weight.

Such that the old person weight is 65 kg.

We have the newly added person weight, so 65 + 20 = 85 kg.

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.

Total weight of 8 persons is 520 (65*8).
Now, a total weight of 7 persons is 455 (520-65),
Now try every option to get 2.5% increase,
(455+85)/8 is equal to 67.5,
The total increase is 2.5 KG (67.5-65),
Ans is 85 KG.

Can you guys tell me about what happens if the weight is decreased by 2.5 kg? Please explain.

Hai Friends.

Try this method.

New person weight =Replaced person weight+ (no. Of persons*increased weight).

Replaced person weight =65.

No. Of persons =8.

Increased weight =2.5.

These all values are replaced in the formula, then we get the answer "85".

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.

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We are adding 20 to 65 because the average weight of 8 persons is being increased to 2.5 kg, by the new person who has been replaced by the existing one.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