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The average of sixteen numbers is 48. The average of the first six of these numbers is 45 and that of the last seven numbers is 53. The seventh and the eighth numbers are, respectively, 3 and 7 greater than the ninth number. What is the average of the ninth and seventh numbers?

The average of sixteen numbers is 48. The average of the first six of these numbers is 45 and that of the last seven numbers is 53. The seventh and the eighth numbers are, respectively, 3 and 7 greater than the ninth number. What is the average of the ninth and seventh numbers? Correct Answer 40.5

Given:

The average of sixteen numbers = 48

The average of the first six numbers = 45

The average of the last seven numbers = 53

Concept used:

Sum of the terms = Average × Number of the terms

Calculation:

Let, the ninth number = x

So, seventh number = x + 3; eighth number = x + 7

Then, x + (x + 3) + (x + 7) = (16 × 48) -

3x + 10 = 768 - (270 + 371)

3x + 10 = 768 - 641

3x = 768 - 641 - 10 = 117

x = 117/3 = 39

∴ The ninth number = 39

∴ The seventh number = 39 + 3 = 42

The average = (39 + 42)/2 = 81/2 = 40.5

∴ The average of the ninth and seventh numbers is 40.5

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