The average of nine numbers is 60, that of the first five numbers is 55 and the next three is 65. The ninth number is 10 less than the tenth number. Then, tenth number is –

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AFCAT 01/2025: 23 January 2025 Shift 2 Memory-Based Paper
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  1. 80
  2. 70
  3. 75
  4. 85

Answer (Detailed Solution Below)

Option 1 : 80
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Given:

Average of nine numbers = 60

Average of first five numbers = 55 and average of next three numbers = 65

Tenth number = Ninth number + 10

Concept used:

Average = Total sum of all numbers / (Count of the numbers)

Calculation:

The sum of nine numbers = 60 × 9 = 540

The sum of the first five numbers = 55 × 5 = 275

The sum of the next three numbers = 65 × 3 = 195

Ninth number = (540 – 275 – 195) = (540 – 470) = 70

∴ Tenth number = 70 + 10 = 80

Mistake PointsWe have details about 10 numbers but the average is given only of 9 

numbers. To calculate the 10th number, we have a relationship that is

the ninth number is 10 less than the tenth number. So after calculating

the 9th number, use this relation to find the next number. Don't take

the average of 10th number. 

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