Kindly Solve This Question
 

a cricketer has certain average for 9 innings. in the tenth inning, he scores 100 runs,thereby increasing his average by 8 runs. his new average is: ??:wait

[QUOTE=mohsy;436731]a cricketer has certain average for 9 innings. in the tenth inning, he scores 100 runs,thereby increasing his average by 8 runs. his new average is: ??:wait[/QUOTE]

Suppose his average for [B][SIZE=4]9[/SIZE][/B] innings is [B][SIZE=3]X[/SIZE][/B]
[B][SIZE=3][/SIZE][/B]
[SIZE=3][SIZE=2]After [B]10th[/B] inning his average becomes[/SIZE][B] = x + 8[/B][/SIZE]
[B][SIZE=3][/SIZE][/B]
[SIZE=3][SIZE=2]Formula for the calculation of average [/SIZE][B] = Sum of All the items / Total Number of the items[/B][/SIZE]

We have effectively two items in this senario

1: 9 innings of X value
2: 10th inning of 100

Put these values in the above formula:

[B](X + 100)/2 = X+8[/B]

Solve this for X
you will arrive at [B]X = 84[/B], you know X is the average of first nine innings.
Hence his new average after 10th inning will be = 84+8=[B]92 [/B]

OR

=(X + 100) /2
= (84+100)/2
[B][U]=92 Ans.[/U][/B]

[QUOTE=Raz;436736]Suppose his average for [B][SIZE=4]9[/SIZE][/B] innings is [B][SIZE=3]X[/SIZE][/B]
[B][SIZE=3][/SIZE][/B]
[SIZE=3][SIZE=2]After [B]10th[/B] inning his average becomes[/SIZE][B] = x + 8[/B][/SIZE]
[B][SIZE=3][/SIZE][/B]
[SIZE=3][SIZE=2]Formula for the calculation of average [/SIZE][B] = Sum of All the items / Total Number of the items[/B][/SIZE]

We have effectively two items in this senario

1: 9 innings of X value
2: 10th inning of 100

Put these values in the above formula:

[B](X + 100)/2 = X+8[/B]

Solve this for X
you will arrive at [B]X = 84[/B], you know X is the average of first nine innings.
Hence his new average after 10th inning will be = 84+8=[B]92 [/B]

OR

=(X + 100) /2
= (84+100)/2
[B][U]=92 Ans.[/U][/B][/QUOTE]



But Brother, if his average prior to scoring 100 in the tenth match was 84, it meant that he would have scored 84*9=756 scores. And after scoring 100 in the tenth inning his total score would have become 756+100=856. And his new average out of 10 matches would be 856/10= 85.6. Which is not 8 more than the previous 84. So the calculations have led to the [B]erroneous[/B] result.

According to me his average of the nine innings was [B]20[/B]. After scoring 100 in the 10th inning his average would become [(20*9)+100]/10 = [B]28[/B].

What do you say sir?:)

The solution would be as follows:
 

Let the total score for first nine innings be[B] 9x.[/B]
Score after the tenth inning will be [B]9x + 100[/B]
Now, the equation would be of the form:

[B]9x/9 +8 = (9x + 100)/10
(9x + 72)/9 = (9x + 100)/10
90x + 720 = 81x + 900
90x minus 81x = 900 minus 720
9x = 180
x = 180/9
x=20[/B]

And the new average would be[B] 20 + 8 = 28[/B]

[QUOTE=mohsy;436731]a cricketer has certain average for 9 innings. in the tenth inning, he scores 100 runs,thereby increasing his average by 8 runs. his new average is: ??:wait[/QUOTE]
his avg increased by 8 runs means that when he scored 100 then according to 10th attempt he get 80 runs extra because these 80 runs in 10 attempts will increase avg by 8 runs and it also means that the remaining 20 runs he score out of 100 was just to maintain the old avg
so the old avg was 20 and the new one (20+8) is 28

another way

20*9=180 runs which he was scoring already
then 100 runs in 10th attempt added
so 180+100=280
now divide 280 on 10 to get new avg = 280/10 = 28

[QUOTE=Faisal86;436745]But Brother, if his average prior to scoring 100 in the tenth match was 84, it meant that he would have scored 84*9=756 scores. And after scoring 100 in the tenth inning his total score would have become 756+100=856. And his new average out of 10 matches would be 856/10= 85.6. Which is not 8 more than the previous 84. So the calculations have led to the [B]erroneous[/B] result.

According to me his average of the nine innings was [B]20[/B]. After scoring 100 in the 10th inning his average would become [(20*9)+100]/10 = [B]28[/B].

What do you say sir?:)[/QUOTE]

Thanks for correction. My solution was outcome of hasty calculation.

You are right.

If the avg of [B]9[/B] innings is x then their [B]sum[/B] will be [B]9X[/B]
Total sum of [B]10[/B] innings will be = [B]9X+100[/B]
[B]Average[/B] of 10 innings will be = X+8

As per formula:

Average = Total Sum / Number
X+8 = (9X+100)/10
Result comes:
X=20
New average will be 20+8=28.

[B][U]Ans: 28[/U][/B]

answer will be [B]28[/B]