Question

The sum of K numbers is 2000 and their average is 50. If 91 is included into the list, then
the new average is
(1) 51
(2) 49
(3) 52
(4) 53

Answer 1

average = sum/ number of numbers
therefore, 50= 2000/k
implies k= 40


if 91 is includes into the list sum becomes 2091 and the number of numbers become 40+1=41.
so new average is 2091/41= 51 ie option a

Answer 2

We know that average is calculated as

$Average = \frac{sum \: of \: all \: numbers}{total \: numbers}$
Total numbers = K

Sum of all K numbers = 2000

Average = 50

Put these values in the above formula,to find K

$50 = \frac{2000}{K} \\ \\ K = \frac{2000}{50} \\ \\ K = 40$
So total number are 40.

Now 91 is added ,thus total numbers becomes 41.

New average
$= \frac{2000 + 91}{41} \\ \\ = \frac{2091}{41} \\ \\ = 51$
Thus, New Average is 51.

Option (1) is correct answer.

Hope it helps you.