Question

there are n numbers when 2 subtract from each of them then these numbers sum are 110 when 5 subtracted these numbers sum is 20, average of n numbers​

Answer 1

Answer:

Sum of n numbers be x

Then x-2n=110

x-5n=20

Solving tem we will get x=170 and n=30 then average =x/n=170/30=17/3

Answer 2

Average of n numbers​ is 17/3.

Let for 'n' numbers the average be 'x'.

So, the total sum of 'n' numbers would be 'nx.'

If 2 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = (2n)

Thus, value of the total sum now = (nx - 2n)

Given that, this value equals to 110.

So, nx - 2n = 110                                                  ...(1)

Again when 5 is subtracted from each 'n' numbers, then the resulted value to be subtracted becomes = (5n)

Thus, value of the total sum now = (nx - 5n)

Given that, this value equals to 20.

So, nx - 5n = 20                                                  ...(2)

Subtracting (2) from (1), we get:

nx - 2n - (nx - 5n) = 110 - 20

⇒ -2n + 5n = 90

⇒ 3n = 90

⇒ n = 90/3 = 30

There are 30 numbers.

Putting n = 30, in eqn.(1), we get:

(30)x - 2(30) = 110

⇒ 30x - 60 = 110

⇒30x = 170

⇒ x = 170/30 = 17/3

Thus the average of 30 numbers is 17/3.