Question

16.The average of 15 numbers is 115. If the average of the first eight numbers is 111 and that of last eight numbers is 120, what is the middle number?​

Answer 1

Solution

Given:-

• The average of 15 numbers is 115.
• the average of the first eight numbers is 111
• Average of last eight numbers is 120

Find :-

• Middle Number

Explantion

Let,

==> x1 , x2, x3, _______x15 be 15 number .

And,

==> x1, x2 , x3, _____x8 be first 8 number .

And,

==> x8, x9, ______x15 be last 8 number

So, according to question

(The average of 15 numbers is 115.)

==> (x1 + x2 + _____ + x15 )/15 = 115

==> (x1 + x2 + ______ + x15 ) = 15 × 115

==> (x1 + x2 + ______ + x15 ) = 1725 _________(1)

Case 1.

(the average of the first eight numbers is 111)

==> (x1 , x2 + ______ + x8 )/8 = 111

==> x1 + x2 + _____ + x8 = 111 × 8

==> x1 + x2 + _______ + x8 = 888____________(2)

Case 2.

(the average of the last eight number is 120)

==> (x8 + x9 + ____ + x15 )/8 = 120

==> x8 + x9 + ______ + x15 = 120 × 8

==> x8 + x9 + _____ + x15 = 960 ___________(3)

Add equ(2) & equ(3)

==> x1 + x2 + ____+ 2x8 + ____ + x15 = 888 + 960

==> x1 + x2 + ____+ 2x8 + ____ + x15 = 1878

Or,

==> x8 + ( x1 + x2 + ______ + x15) = 1878_______(4)

keep value by equ(1)

==> x8 + 1725 = 1878

==> x8 = 1878 - 1725

==> x8 = 153

Hence

• Value of middle Number be = 153

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