The average of 13 numbers is 84. The average of the first five numbers is 60. The average of the next five numbers is 30% higher than the first five. The 11th number is 6 less than the 13th number, and the 12th number is 6 more than the 13th number. Find the average of the 11th and 12th numbers.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 134.
Sum of 13 numbers = 13 × 84 = 1092
Sum of first 5 numbers = 5 × 60 = 300
Average of next 5 numbers = 60 × (130/100) = 78
Sum of next 5 numbers = 5 × 78 = 390
Sum of first 10 numbers = 300 + 390 = 690
Sum of last 3 numbers = 1092 - 690 = 402
Let the 13th number = x
11th number = x - 6
12th number = x + 6
So, (x - 6) + (x + 6) + x = 3x = 402
⇒ x = 402/3 = 134
Average of 11th and 12th numbers = [(x - 6) + (x + 6)]/2 = (2x)/2 = x = 134