The average of twelve numbers is 46. The average of the first four numbers is 43 and that of the last five numbers is 49.4. The 5th and the 6th numbers are respectively 4 and 6 more than the 7th number. What is the average of the 5th and 7th numbers?

The average of twelve numbers is 46. The average of the first four numbers is 43 and that of the last five numbers is 49.4. The 5th and the 6th numbers are respectively 4 and 6 more than the 7th number. What is the average of the 5th and 7th numbers? Correct Answer 43

Average of 12 numbers = 46

⇒ Sum of all 12 numbers = 12 × 46 = 552

Average of the first 4 numbers = 43

⇒ Sum of first 4 numbers = 4 × 43 = 172

Average of the last five numbers = 49.4

∴ Sum of the last five numbers = 247

Let the 7^th number be x.

∴ 5^th number will be = x + 4

∴ 6^th number will be = x + 6

Sum of 5^th, 6^th and 7^th number = 552 – 172 – 247 = 133

According to the question

⇒ x + x + 4 + x + 6 = 133

⇒ x = 41

⇒ 7^th number = 41

⇒ 5^th number = x + 4 = 41 + 4 = 45