The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The 10th number is 4 more than the 11th number and 9 more than the 12th number. What is the average of the 10th and 12th numbers?

The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The 10th number is 4 more than the 11th number and 9 more than the 12th number. What is the average of the 10th and 12th numbers? Correct Answer 46.5

Average of 12 numbers in = 45.5

Sum of 12 numbers = 45.5 × 12 = 546

Average of first 4 numbers = 41.5

Sum of first 4 numbers = 41.5 × 4 = 166

Average of next 5 numbers = 48

Sum of next 5 numbers = 48 × 5 = 240

Sum of 10^th, 11^th and 12^th number = 546 – 166 – 240 = 140

Let the 10^th number be x

11^th number = x – 4

12^th number = x – 9

According to the question

x + x – 4 + x – 9 = 140

⇒ 3x – 13 = 140

⇒ 3x = 140 + 13

⇒ 3x = 153

∴ x = 153/3 = 51