The average of 24 numbers is 26. The average of the first 15 numbers is 23 and that of the last 8 number is 33. Find 16th number.
A16
B15
C17
D18
Answer:
B. 15
Read Explanation:
Solution:
Given:
Average of 24 numbers = 26
Average of 1st 15 numbers = 23
Average of last 8 numbers = 33
Concept:
Subtract the sum of the first 15 numbers and the last eight numbers from the sum of all 25 numbers to get the sixteenth number.
Formula used:
Average = (Sum of all values)/Total number of values
Sum of all values = (Average) × (Total number of values)
Calculation:
∵ The average of 24 numbers = 26
∴ Sum of 24 numbers = 26 × 24 = 624
∵ The average of 1st 15 numbers = 23
∴ Sum of 1st 15 numbers = 23 × 15 = 345
∵ The average of last 8 numbers = 33
∴ The sum of last 8 numbers = 33 × 8 = 264
16th Number = (Sum of 24 numbers) - (Sum of 1st 15 numbers + sum of last 8 numbers)
⇒ 624 - (345 + 264)
⇒ 624 - 609
⇒ 15
∴ The correct answer is 15.
