Question

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.

• A. 16
• B. 15
• C. 17
• D. 18

Answer 1

Answer:

B. 15

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.