Arithmatic mean

Question

the arithmetic mean of 25 numbers is 36. if arithmetic mean of first 13 and last 13 numbers are 32 and 39 respectively, find the 13th number

Answer 1

Let 13th number = x

Arithemetic mean of 25 numbers is 36 = 25*36 = 900

Arthemetic mean of first 13 numbers 32

The sum of  13 numbers = 32*13 = 416

The sum of first 12 numbers = 416-x

The mean of last i3 numbers = 39

The sum of last 13 numbers =39*13 = 507

The sum of last 12 numbers = 507-x

There fore (416-x)+x+(507-x) = 900

923-x = 900

Subtract 900 from each side.

923-900-x = 900-900

23 -x =  0

Subtract 23 from each side.

23-23-x = 0-23

-x = -23

Cancell the signs to each side.

x = 23

Therefore13th number is 23.