The average of eleven numbers is 68. The average of the first four numbers is 78 and that of the next four numbers is 63. The 9th number is two times the 11th number and the 10th number is 4 less than the 11th number. What is the average of the 9th and 11th number?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 70.5
Sum of 11 numbers = 11 × 68 = 748
Average of 1st four numbers = 78
So,
Sum of 1st four numbers = 78 × 4 = 312
Average of next four number = 63
Sum of next four numbers = 63 × 4 = 252
Let the 11th number = x
So, 9th number = 2x
10th number (4 less than the 11th number) = x - 4
So,
Sum of 9th, 10th, and 11th numbers = x + 2x + x - 4 = 748 - (312 + 252)
⇒ 4x - 4 = 184
⇒ x = 47
So,
Average of 9th and 11th numbers = (47 + 94)/2 = 70.5