Aptitude - Average - Discussion

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

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.

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

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".

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.

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.

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.

There is very simple formula for this.

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

So, 8 * 2.5 + 65 = 85.

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