Question

Average of 8 numbers is 52, and the average of first three numbers is 50, and the average of next two numbers is 54, the seventh number is 5 more than the sixth number and 2 more than the eighth number. What is the average of the seventh and the eighth number?

1. 54
2. 50
3. 53
4. 55

Answer 1

Correct Answer - Option 1 : 54

Given:

Average of all eight numbers = 52

Average of first three numbers = 50

Average of next two numbers = 54

Seventh number is 5 more than sixth number

Seventh number is 2 more than eighth number

Formula used:

Sum of all observations = Average × Number of observations

Calculation:

Sum of all numbers = 52 × 8 = 416

Sum of first three numbers = 50 × 3 = 150

Sum of next two numbers = 54 × 2 = 108

Let seventh number be x, sixth number be x – 5, and eighth number be x – 2

Sum of all numbers = 150 + 108 + x – 5 + x + x – 2

⇒ 416 = 251 + 3x

⇒ 3x = 416 – 251 = 165

⇒ x = 55

Seventh term = 55

Eighth term = 53

Average of seventh and eighth term = (55 + 53)/2

∴ Average of seventh and eighth term is 54