The average of 8 numbers is 19. The average of first and sixth numbers is 17 and that of the third, fifth and seventh numbers is \(24\frac{1}{3}\). If the second number is less than the fourth number by 8, and greater than the eighth number by 2, then the sum of fourth number and eighth number is:
The average of 8 numbers is 19. The average of first and sixth numbers is 17 and that of the third, fifth and seventh numbers is \(24\frac{1}{3}\). If the second number is less than the fourth number by 8, and greater than the eighth number by 2, then the sum of fourth number and eighth number is:
1). 45
2). 21
3). 13
4). 32
1 answers
We know that, Average = Sum of all observations/Number of observations
According to the given information,
Average of 8 numbers is 19
? The average of first and sixth numbers is 17
first number + sixth number = 17 × 2 = 34
And, since Average of the third, fifth and seventh numbers is $(24\frac{1}{3})$
∴ third number + fifth number + seventh number $(= \;24\frac{1}{3}\; \times 3\; = \;73)$
Now, since the second number is less than the fourth number by 8, and greater than the eighth number by 2, let the second number be x thus, fourth number would be x + 8, and eighth number would be x - 2.
Thus,
19 = (sum of all eight numbers)/8
$(\Rightarrow \frac{{x\; + \;x\; + \;8\; + \;x\; - \;2\; + \;73\; + \;34\;}}{8} = 19)$
⇒ 3x + 113 = 152
⇒ 3x = 39
⇒ x = 13
Hence fourth number = 13 + 8 = 21
eighth number = 13 - 2 = 11
Required sum = 21 + 11 = 32