Problem Solving

9. A baseball team averages x runs per game in the first n games. If the team then scores y runs in the next game, by how much is the average number of runs per game then changed ?

(a) (y – x)/(n + 1)
(b) (y – x)/n
(c) y/(n + 1) – x/n
(d) y/n – x/(n + 1)
(e) 2(y – x)/((2n + 1)

Average for n games = x = Total runs/total matches = T/n -- (1)
From (1) Total runs for n games T=nx. Now in the next game the team scores y runs so the Total runs for n+1 games = (nx+y).

Hence the Average for n+1 games = (nx+y)/(n+1) --- (2)
(2)-(1)=Average of n+1 games - Avg of n games is the change in average = (nx+y)/(n+1) - x = (y-x)/(n+1) = A.)

- Deepak

I like more formulas, so will include the explanation that is clearer to me If a1..an - runs per games 1..n accordingly then

(a1+..+an)/n = x - average for n games
(a1+..+an+y)/(n+1) = (nx+y)/(n+1) - average for n+1 games

And yes, it was said we need to find the difference so answer is A

Folks, this can be answered without any calculations.....

The change (increase/decrease) in the number of the runs is y - x. This will be shared by the total n+1 matches. Hence the change in the avg is (y-x)/n+1.

For ex: The avg weight of 24 students is 62 kgs. If a student whose weight is 72 kgs joins the class, what will be the avg weight of the present class.

Sol: If the weight of the new student is also 62, the avg of the present 25 students will remain 62. But since the weight of the new student is 72, i.e there is a gain of 10 kgs in the weight and this gain will be shared by the present class.

So the increase in the avg is 10/25.

Hence the avg of the present class = 62 + 10/25 = 62.4 kgs


(Note: If x > y, there will be a loss in the avg )

For more tips to solve questions on averages quickly go through the link in my signature below