The average of nine numbers is 50. The average of the first five numbers is 54 and the average of the last three numbers is 52. Find the sixth number of this set of numbers?

24

The correct answer is Option (1) → 24

1. Calculate the total sum of all nine numbers:

$\text{Sum of 9 numbers} = \text{Average} \times \text{Total numbers}$

$\text{Sum} = 50 \times 9 = \mathbf{450}$

2. Calculate the sum of the first five numbers:

$\text{Sum of first 5 numbers} = 54 \times 5 = \mathbf{270}$

3. Calculate the sum of the last three numbers:

$\text{Sum of last 3 numbers} = 52 \times 3 = \mathbf{156}$

4. Find the sixth number:

The sum of all nine numbers is the sum of the first five, the sixth number, and the last three.

$\text{Total Sum} = (\text{Sum of first 5}) + (\text{6th number}) + (\text{Sum of last 3})$

$450 = 270 + \text{6th number} + 156$

$450 = 426 + \text{6th number}$

$\text{6th number} = 450 - 426 = \mathbf{24}$