The average of eleven numbers is 56. The average of first three numbers is 52 and that of next five numbers is 60. The 9th and 10th number are 3 and 1 more than the 11th number prespectively. What is the average of 9th and 11th numbers?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 53.5
Sum of all observations = Average × number of observations
⇒ Sum of 11 numbers = 56 × 11
⇒ 616
Sum of first 3 numbers = 3 × 52
⇒ 156
The sum of 4th to 8th number = 5 × 60
⇒ 300
Sum of 9th, 10th , and 11th number is = 616 - (156 + 300)
⇒ 616 - 456 = 160
Let the 11th number be 'x'
⇒ 9th number = x + 3
⇒ 10th number = x + 1
⇒ x + x + 1 + x + 3 = 160
⇒ 3x + 4 = 160
⇒ x = 52
Average of 9th and 11th number: (55 + 52)/2
⇒ 53.5