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The average of fourteen numbers is 46. The average of first five is 43 and that of last six numbers is 49.5. The sixth and seventh numbers are respectively 4 and 8 greater than the eighth number. What is the average of sixth and seventh numbers?

The average of fourteen numbers is 46. The average of first five is 43 and that of last six numbers is 49.5. The sixth and seventh numbers are respectively 4 and 8 greater than the eighth number. What is the average of sixth and seventh numbers? Correct Answer 46

Average of 14 numbers = 46

Sum of 14 numbers = 46 × 14 = 644

Average of first 5 numbers = 43

Sum of first 5 numbers = 43 × 5 = 215

Average of last six numbers = 49.5

Sum of last six numbers = 49.5 × 6 = 297

Sum of 6th, 7th and 8th number is = 644 – 215 – 297 = 132

Let the eight number be x, then

Sixth and seventh numbers are (x + 4) and (x + 8) respectively.

x + 4 + x + 8 + x = 132

3x + 12 = 132

3x = 132 – 12

x = 120/3

x = 40

Sixth number = 40 + 4 = 44

Seventh number = 40 + 8 = 48

Average of sixth and seventh numbers = (44 + 48)/2 = 46

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