Question

The average of 9 nos is 50 . The average of first 5 no is 54 and that of the last 3 no is 52 then the sixth no is ?

• A. 20
• B. 24
• C. 26
• D. 29

Answer 1

Answer:

B. 24

• To find the missing number, we need to utilize the relationship between the average, the sum, and the number of observations.

• First, calculate the total sum of all 9 numbers:

  • Given: Average of 9 numbers = 50.

  • Sum of 9 numbers = Average × Number of observations = 50 × 9 = 450.

• Next, calculate the sum of the first 5 numbers:

  • Given: Average of first 5 numbers = 54.

  • Sum of first 5 numbers = 54 × 5 = 270.

• Then, calculate the sum of the last 3 numbers:

  • Given: Average of last 3 numbers = 52.

  • Sum of last 3 numbers = 52 × 3 = 156.

• The total sum of the 9 numbers (450) is composed of the sum of the first 5 numbers, the 6th number, and the sum of the last 3 numbers.

• Therefore, the 6th number can be found by subtracting the sum of the first 5 and the sum of the last 3 numbers from the total sum of all 9 numbers.

• Sixth number = (Sum of 9 numbers) - (Sum of first 5 numbers + Sum of last 3 numbers)

• Sixth number = 450 - (270 + 156)

• Sixth number = 450 - 426 = 24.