Question

The average of 24 numbers is 65. The average of first 11 numbers is 67 and the average of last 10 numbers is 70. If the 12th number is 13 less than the 13th number, and the 14th number is one more than the 13th number, then the average of 12th and 14th number is:

​

Answer 1

Step-by-step explanation:

24=65 11=67 10=70 thus 12 or 14 number =81

Answer 2

The average of 12th and 14th number is 39.

Step-by-step explanation:

Since we have given that

Numbers = 24

Average = 65

So, Sum of 24 observations = $24\times 65=1560$

Average of first 11 numbers = 67

So, Sum of first 11 observations = $67\times 11=737$

Average of last 10 number = 70

So, Sum of first 10 observations = $10\times 70=700$

Let the 13th number be 'x'.

Let the 12th number be 'x-13'

Let the 14 th number be 'x+1'

So, it becomes,

Sum of first 11 numbers + x+ x-13+ x+1+ sum of last 10 numbers = 1560

$737+x+x-13+x+1+700=1560\\\\1437+3x-12=1560\\\\3x=1560-1437+12\\\\3x=135\\\\x=\dfrac{135}{3}\\\\x=45$

So, the 12th number  = 45-13 = 32

The 14th number = 45+1=46

So, the average of 12th and 14th number is

$\dfrac{46+32}{2}=\dfrac{78}{2}=39$

Hence, the average of 12th and 14th number is 39.

# learn more:

The average of 25 numbers is 18 .if the average of first 12 numbers is 14 and that of the last 12 is 17, then the 13th numbers is:

https://brainly.in/question/1989887