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The average of 8 numbers is 47, and the average of the first three numbers is 39, and the average of the next two numbers is 48, the seventh number is 2 more than the sixth number and 3 less than the eighth number. What is the average of the sixth and the seventh number?

The average of 8 numbers is 47, and the average of the first three numbers is 39, and the average of the next two numbers is 48, the seventh number is 2 more than the sixth number and 3 less than the eighth number. What is the average of the sixth and the seventh number? Correct Answer 53

Given:

Average of all eight numbers = 47

Average of first three numbers = 39

Average of next two numbers = 48

Seventh number is 2 more than sixth number

Seventh number is 3 less than eighth number

Formula used:

Average = Sum of all the terms/Number of all the terms

Calculation:

Sum of all numbers = 47 × 8 = 376

Sum of first three numbers = 39 × 3 = 117

Sum of next two numbers = 48 × 2 = 96

Let seventh number be x, sixth number be x – 2, and eighth number be x + 3

Sum of all numbers = 117 + 96 + x – 2 + x + x + 3

⇒ 214 + 3x = 376

⇒ 3x = 162

⇒ x = 54

Seventh number = 54

Sixth number = 54 – 2 = 52

Average of sixth and seventh number = (54 + 52)/2

∴ The average of sixth and seventh number is 53

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