The average of ten numbers is 7. If each number is multiplied by 12, then the average of the new set of numbers is

Options

A. (a) 7
B. (b) 19
C. (c) 82
D. (d) 84

Answer

To solve the problem step-by-step, we can follow these instructions:

### Step 1: Determine the sum of the original numbers
The average of ten numbers is given as 7. To find the sum of these numbers, we can use the formula for average:

\[ \text{Average} = \frac{\text{Sum of numbers}}{\text{Number of items}} \]

Rearranging this formula gives us:

\[ \text{Sum of numbers} = \text{Average} \times \text{Number of items} \]

Substituting the given values:

\[ \text{Sum of numbers} = 7 \times 10 = 70 \]

### Step 2: Calculate the sum after multiplying each number by 12
If each of the ten numbers is multiplied by 12, the new sum can be calculated as follows:

\[ \text{New Sum} = \text{Original Sum} \times 12 \]

Substituting the original sum:

\[ \text{New Sum} = 70 \times 12 = 840 \]

### Step 3: Calculate the new average
To find the new average after multiplying each number by 12, we again use the formula for average:

\[ \text{New Average} = \frac{\text{New Sum}}{\text{Number of items}} \]

Substituting the new sum and the number of items:

\[ \text{New Average} = \frac{840}{10} = 84 \]

### Final Answer
Thus, the average of the new set of numbers is **84**.

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