Question

The average of 17 numbers is 27. If the average of first 8 numbers is 22 and
the average of last 8 numbers is 33, then find the value of middle number.
(A) 29
(B) 22
(C) 27
(D) 19
(E) None of these​

Answer 1

Answer:

Step-by-step explanation:

The middle number is none of these

Answer 2

Answer:

The middle term is 19

Answer: D) 19

Step-by-step explanation:

The average of 17 numbers is 27.

Average = Sum of numbers/total numbers

27 = Sum of numbers/17

Sum of numbers = 27×17

Sum of numbers = 459 ............ (1)

The average of first 8 numbers is 22

Average = sum of numbers/total numbers

22 = sum of numbers/8

sum of numbers = 22×8

Sum of first 8 numbers = 176 ....... (2)

The average of last 8 numbers is 33

Average = Sum of numbers/total numbers

33 = Sum of numbers/8

Sum of numbers = 33×8

Sum of last 8 numbers = 264 ......... (3)

Let the middle number be 'x'

Sum of all numbers = Sum of first 8 numbers+Sum of last 8 numbers+x

459 = 176+264+x

x = 459-176-264

x = 19

Therefore, the middle term is 19.