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The average of 17 numbers is 55. The average of the first 6 numbers is 49.5 and that of the next 8 numbers is 60.5. The 16th number is 4 less than the 15th number and 6 less than the 17th number. What is the average of the 15th and 17th numbers?

The average of 17 numbers is 55. The average of the first 6 numbers is 49.5 and that of the next 8 numbers is 60.5. The 16th number is 4 less than the 15th number and 6 less than the 17th number. What is the average of the 15th and 17th numbers? Correct Answer 53

Given:

The average of 17 numbers = 55

The average of the first 6 numbers = 49.5

The average of the next 8 numbers = 60.5

16th number = 15th number - 4

16th number = 17th number - 6

Formula Used:

Average = Sum of the observations/Total number of observations

Calculation:

According to the questions,

The average of 17 numbers = 55

Sum of 17 numbers = 55 × 17

⇒ 935

The average of the first 6 numbers = 49.5

Sum of first 6 numbers = 49.5 × 6

⇒ 297

The average of the next 8 numbers = 60.5

Sum of next 8 numbers = 60.5 × 8

⇒ 484

Hence, the sum of 15th, 16th and 17th number = 935 - 297 - 484 

⇒ 154

Let the 16th number be x, then

16th number = 15th number - 4

⇒ 15th number = x + 4

16th number = 17th number - 6

⇒ 17th number = x + 6

Hence, 15th number + 16th number + 17th number = 154

⇒ (x + 4) + x + (x + 6) = 154

⇒ 3x = 154 - 10

⇒ x = 48

The average of the 15th and 17th number 

⇒ (x + 4 + x + 6)/2

⇒ (48 + 4 + 48 + 6)/2

⇒ 106/2 = 53

∴ The average of the 15th and 17th numbers is 53.

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