Question

The average of 17 results is 60. If the average of first 9 results is 57 and that of the last 9 results is 65, then what will be the value of 9th result?

A) 39 B) 78 C) 117 D) 156

Answer 1

In the above Question , the following information is given -

The average of 17 results is 60.

The average of first 9 results is 57 and that of the last 9 results is 65.

To find -

What will be the value of 9th result?

Solution -

Here ,

The average of 17 results is 60.

The average of first 9 results is 57 and that of the last 9 results is 65.

First let me define what is average .

For a n number of results , average refers to the mean value of them .

So ,

It can be written as -

Average = [ Sum of n number of results ] / n .

Case 1 -

The average of first 9 results is 57

[ Sum of first 9 results ] / [ 9 ] = 57

=> Sum of first 9 results -

=> 9 × 57

=> 513 .

Now ,

The average of first 9 results is 57

[ Sum of first 9 results ] / [ 9 ] = 57

=> Sum of first 9 results -

=> 9 × 57

=> 513 .

Now ,

The average of lawt 9 results is 65

[ Sum of last 9 results ] / [ 9 ] = 65

=> Sum of last 9 results -

=> 65 × 9

=> 585 .

Now ,

Let us add this two values -

LHS -

[ Sum of first 9 results ] + [ Sum of second 9 results ]

=> [ Sum of first 8 results ] + ] Sum of second 9 results ] + 2 × 9 the result

=> [ Sum of first 8 results ] + ] Sum of second 9 results ] + 9 th result + 9 th result

=>{ [ Sum of first 8 results ] + ] Sum of second 9 results ] + 9 th result } + 9 th result

=> Sum of first 17 results + 9 th result.

RHS -

=> 513 + 585

=> 1098

Now ,

The average of 17 results is 60

=> Sum of 17 results -

=> 17 × 60

=> 1120

9 th result -

=> ∆ r

=> 1120 - 1098

=> 32 .

This is the required answer .

__________________

Answer 2

$\huge\sf\pink{Answer}$

☞ Option B

$\rule{110}1$

$\huge\sf\blue{Given}$

✭ The Average of 17 results is 60

✭ Average of first 9 results is 57

✭ Last 9 average is 65

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

◈ Value of the 9th result

$\rule{110}1$

$\huge\sf\purple{Steps}$

$\bullet\underline{\textsf{As Per the Question}}$

➝ Average of total = 17×6 = 1020

➢ Average of first 9 results = 9×57 = 513

≫ Average of last nine results = 9×65 = 585

So now,

➳ $\small\sf 9^{th} = Average \ of \ First 9 - Average \ of \ last \ 9 - Total \ Average$

$\sf\rightarrowtail 9^{th} = 1020-513-585$

$\sf\orange{\rightarrowtail 9_{term} = 78}$

$\rule{170}3$