Multiple choice

The average of ten numbers is 72. The average of the first four numbers is 69 and that of the next three numbers is 74. The 8th number is 6 more than the 9th number and 12 more than the 10th number. What is the average of the 8th and 9th numbers?

  1. 76

  2. 76.5

  3. 77.5

  4. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total sum = 10 * 72 = 720. Sum of first 4 = 4 * 69 = 276. Sum of next 3 = 3 * 74 = 222. Sum of last 3 = 720 - 276 - 222 = 222. Let 10th number be x. 8th = x+12, 9th = x+6. (x+12) + (x+6) + x = 222 => 3x + 18 = 222 => 3x = 204 => x = 68. 8th = 80, 9th = 74. Average = (80+74)/2 = 77.

AI explanation

The total sum of all ten numbers is 10 * 72 = 720. The sum of the first four is 4 * 69 = 276, and the sum of the next three is 3 * 74 = 222. The sum of the last three numbers is 720 - 276 - 222 = 222. If the 10th number is x, the 9th is x + 6, and the 8th is x + 12; their sum is 3x + 18 = 222, which makes x = 68. The 8th number is 80 and the 9th is 74, so their average is (80 + 74) divided by 2, which equals 77.

Keep practicing — related questions