The average of 18 numbers is 52. The average of the first 8 numbers is 62 and the average of the next 7 numbers is 45. If the 16th number is 6 less than the 17th number and the 17th number is one more than the 18th number, then what is the average of the 16th and 18th number?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e 40.5
⇒ The average of 18 numbers is 52
Sum of 18 numbers = 52 × 18 = 936
⇒ The average of the first 8 numbers is 62
Sum of first 8 numbers = 62 × 8 = 496
⇒ The average of the next 7 numbers is 45
Sum of next 7 numbers = 7 × 45 = 315
So, the sum of 16 to 18 number = 936 - (496 + 315) = 125
Let the 17th number = x
So the 16th number = x - 6
and the 18th number = x - 1
So,
x - 6 + x + x - 1 = 125
⇒ 3x = 132
⇒ x = 132/3 = 44
So the 16th number = 44 - 6 = 38
and the 18th number = 44 - 1 = 43
Hence,
Average of 16th and 18th number = (38 + 43)/2 = 40.5