The average of sixteen numbers is 48. The average of the first six of these numbers is 45 and that of the last seven numbers is 53. The seventh and the eighth numbers are, respectively, 3 and 7 greater than the ninth number. What is the average of the ninth and seventh numbers?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 40.5.
Let's assume the ninth number = x
Seventh number = x + 3, and Eighth number = x + 7
We know that,
Average = Sum of observations/Number of observations
The sum of the 16 numbers = 16 × 48 = 768
The sum of the first 6 numbers = 6 × 45 = 270
The sum of the last seven number = 7 × 53 = 371
Then,
⇒ x + x + 3 + x + 7 = 768 - (270 + 371)
⇒ 3x + 10 = 768 - 641
⇒ x =
⇒ x = 39
Ninth number = x = 39, and Seventh number = x + 3 = 42
Average = = 40.5
Hence, the average of the ninth and seventh numbers is 40.5