Question

The average of 15 numbers is 18. The average of first 8 is 19 and that last 8 is 17, then the 8th number is

Answer 1

The  $8^{th}$ number is 10.

• The average of 15 numbers is 18.

• The average of first 8 numbers is 19 and the average of last 8 numbers is 17.

We have to find the $8^{th}$ number.

• Let the eighth number be x.

• Now ,

Average of first 8 numbers = 19

(Sum of first 7 + x) / 8 = 19

(Sum of first 7 + x) = 152                         (Equation 1)

• Now, Average of last 8 numbers = 17

(x + sum of last 7 numbers) / 8 =  17

Sum of last 7 numbers + x = 136             (Equation 2)

• Now average of all the numbers = 18

(Sum of 15 numbers) / 15 = 18

Sum of 15 numbers = 270

Sum of first 7 numbers + x + Sum of last 7 numbers = 270      (Equation 3)

• Now, adding equation 1 and equation 2 we get

Sum of first 7 numbers + x + x + Sum of last 7 numbers = 152 + 136

Sum of first 7 numbers + x + x + Sum of last 7 numbers = 288

• Now ,

x + 270 = 280                      (From equation 3)

x = 10

• The value of  $8^{th}$ number is 10.