Aptitude - Average - Discussion

why we took 9(x-1) here? Please explain.

Can anyone explain using distribution method?

A captain age is 26 years old.

Then wicket keeper is 3 years older than as captain. So (26+3)=29.
Total= avg* no of observation,
x= 11 players average, y= total of 9 players.
At 11players,
y+26+29= x* 11.
y+55= 11x -----------> (1)
At 2 players excluded, so 9 players,
As formula. y= (x-1)* 9 -----------> (2)
(2) substituting by (1):

(x-1)* 9+55= 11x,
9x-9+55= 11x,
2x= 46,
X= 23.

So average of whole team so 23 years old.

If we assume c be the avg of the whole team then why 11x-55 why not x-55?

Thanks all of you.

How 9 will come can you explain detail?

Let 9 Players Avg = P9
Let 11 Players Avg = x

So,
(P9 + 26 + 29) / 11 = x ------------> (Eq 1)

P9 / 9 = x -1 (Total Average is less than 1 if we exclude 26 (Cap.) and 29 (Wk))

or x = 1 + (P9 / 9) ===== or ==== x = ( P9 + 9 ) / 9 -------------> (Eq 2)

Put x value from Eq 2 to Eq 1

(P9 + 26 + 29) / 11 = ( P9 + 9 ) / 9

9 P9 + 234 + 261 = 11 P9 + 99 --------> Cross Multiplication
11 P9 - 9 P9 = 234 + 261 -99 = 495 - 99 = 396
2 P9 = 396
P9 = 198

Average of 9 Players is 198

Average of 11 Players is = (198 + 26 + 29) / 11
= 253 / 11
= 23

Team Average is 23.

Hope it is helpful to understand.

It's very easy.

11 members players age average - WK age.
26 - 3 = 23.

Explaination:

Number-----------Average -----------Total
11 ----------- x -----------11x
9 ----------- x-1 ----------- 9(x-1).
So, for average of the team :-
11x - (captain + wicketkeeper) = 9(x-1)
hence,
11x - (26+29)=9(x-1),
11x -55 = 9x - 9,
11x - 9x = 46,
2x = 46,
x=23.

Can you explain how to come 9 (x-1)?