Questions :
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.
Options :
- 134
- 136
- 140
- 142
correct answer : a)
Explanation :
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
Therefore, sum of 11th, 12th and 13th numbers = 1092 − 690 = 402
Let the 13th number be x.
Then,
11th number = x − 6
12th number = x + 6
So,
(x − 6) + (x + 6) + x = 402
⇒ 3x = 402
⇒ x = 134
Therefore,
11th number = 128
12th number = 140
Average of 11th and 12th numbers = (128 + 140)/2
= 268/2
= 134
Therefore, the correct answer is option (a) 134. The values 136, 140, and 142 do not satisfy the given conditions and are therefore incorrect.