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The average of fifteen numbers is 49. The average of the first four numbers is 51 that of next eight numbers is 47. The 13th number is two times the 14th number is 3 less than the 15th number. What is the average of 13th and 15th numbers?

The average of fifteen numbers is 49. The average of the first four numbers is 51 that of next eight numbers is 47. The 13th number is two times the 14th number is 3 less than the 15th number. What is the average of 13th and 15th numbers? Correct Answer 58.5

Average of 15 numbers = 49

Sum of 15 numbers = 49 × 15 = 735

The average of first 4 numbers = 51

Sum of first 4 numbers = 51 × 4 = 204

Average of next 8 numbers = 47

Sum of next 8 numbers = 47 × 8 = 376

Sum of 13th, 14th and 15th numbers = 735 – 204 – 376 = 155

Let the 14th number be x

13th number = 2x

15th number = x + 3

According to the question

x + 2x + x + 3 = 155

⇒ 4x = 155 – 3

⇒ 4x = 152

⇒ x = 152/4 = 38

⇒ 13th number = 2 × 38 = 76

⇒ 15th number = 38 + 3 = 41

∴ Average of 13th and 14th number = (76 + 41)/2 = 58.5

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