The average of 10 quantities is 12. The average of 6 of them is 8. What is the average of remaining four numbers.

Answer

To solve the problem step by step, we will use the formula for average and perform calculations based on the information given.

### Step 1: Calculate the sum of the 10 quantities.
The average of 10 quantities is given as 12. We can use the formula for average:

\[ \text{Average} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

From this, we can rearrange the formula to find the sum:

\[ \text{Sum of all observations} = \text{Average} \times \text{Number of observations} \]

Substituting the values:

\[ \text{Sum of 10 quantities} = 12 \times 10 = 120 \]

### Step 2: Calculate the sum of the 6 quantities.
The average of 6 of these quantities is given as 8. Again, we use the average formula:

\[ \text{Sum of 6 quantities} = 8 \times 6 = 48 \]

### Step 3: Calculate the sum of the remaining 4 quantities.
Now, we need to find the sum of the remaining 4 quantities. We can do this by subtracting the sum of the 6 quantities from the sum of the 10 quantities:

\[ \text{Sum of remaining 4 quantities} = \text{Sum of 10 quantities} - \text{Sum of 6 quantities} \]

Substituting the values we calculated:

\[ \text{Sum of remaining 4 quantities} = 120 - 48 = 72 \]

### Step 4: Calculate the average of the remaining 4 quantities.
Now that we have the sum of the remaining 4 quantities, we can find their average:

\[ \text{Average of remaining 4 quantities} = \frac{\text{Sum of remaining 4 quantities}}{4} \]

Substituting the sum we found:

\[ \text{Average of remaining 4 quantities} = \frac{72}{4} = 18 \]

### Final Answer:
The average of the remaining four numbers is **18**.

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