A batsman makes a score of 270 runs in the 87^th inning and thus increase his average by a certain number of runs that is a whole number. Find the possible values of the new average.

To solve this problem, we can use the formula for average:

Average = Total runs / Number of innings

Let's assume the batsman's original average was A. Therefore, the total runs before the 87th inning would be A * (87 - 1) = 86A.

After the 87th inning, the batsman scored an additional 270 runs. So the new total runs would be 86A + 270.

The new average can be calculated by dividing the new total runs by the new number of innings (87):

New Average = (86A + 270) / 87

Given that the new average is a whole number, the numerator (86A + 270) must be divisible by the denominator (87).

To find the possible values of the new average, we need to check whether each option (98, 184, 12) satisfies this condition.

Let's check each option one by one:

A. 98:
If the new average is 98, then (86A + 270) / 87 = 98.
Rearranging the equation, we have 86A + 270 = 98 * 87.
Simplifying, we get 86A + 270 = 8526.
Subtracting 270 from both sides, we have 86A = 8256.
Dividing both sides by 86, we get A ≈ 96.14.
Since A is not a whole number, option A is not valid.

B. 184:
If the new average is 184, then (86A + 270) / 87 = 184.
Rearranging the equation, we have 86A + 270 = 184 * 87.
Simplifying, we get 86A + 270 = 16008.
Subtracting 270 from both sides, we have 86A = 15738.
Dividing both sides by 86, we get A ≈ 182.95.
Since A is not a whole number, option B is not valid.

C. 12:
If the new average is 12, then (86A + 270) / 87 = 12.
Rearranging the equation, we have 86A + 270 = 12 * 87.
Simplifying, we get 86A + 270 = 1044.
Subtracting 270 from both sides, we have 86A = 774.
Dividing both sides by 86, we get A ≈ 9.
Since A is a whole number, option C is valid.

Therefore, the possible value for the new average is 12.

The correct answer is: C. 12

let x be the average for 86 innings.
total score for 86 innings=86x
let y be the increment in the average., then
new average =x+y
(86x+270)/87= x+y
CASE 1:
suppose x+y=12
then, (86x+270)/87 = 12
=> 86x+270=1044
=> 86x= 774
=> x= 774/86=9
i.e, avg for the first 86 inning is 9,
then new avg is increased by 3 which is a whole number
true for this case.
CASE 2:
if x+y= 98
then, (86x+270)/87 = 98
=> x= 96
which is again possible for the average of the first 86 innings.
CASE 3;
if x+y= 184
then then, (86x+270)/87 =184
=> x= 183
which is again possible, i.e, the previous average is increased by 1 which is a whole number.
thus, the final answer is all of the above.

ALTERNATIVELY,
we have, x= avg for the first 86 innings, y= increased in average
then, x-y= no. of increment in average
obviously, x-y>0 [since average cannot be negative]
=> x>y
which means that if y is a whole number, then x value must be whole number.
then, new average can be any whole number such as 98,184,12....
THUS, answwer is all of the above

let x be runs scored in 86 innings and y be average of 86 innings
x/86 = y
after 87th inning , let w be increase in average
(x+270)/87 = y+w
y+w =270-86*w
put w=1,2,3 => you will get 184,98,12 as y
so , answer is all of these

Shephali Swarnkar
86*9+270/87= 12.....
so, answer all of these

Answer should be none(E). As the formula would be (86*N + 270)/87 = Number divisible by 87. none of the given number returns a whole number when putting in place of 'N'.

Can anyone provide a more detailed working for this?

please give question in hindi