The average of six numbers is 20. If one number is removed, the average becomes 15. What is the number removed ?

Options

A. 5
B. 35
C. 112
D. 45

Answer

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

### Step 1: Calculate the total of the six numbers
The average of six numbers is given as 20. The formula for average is:

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

From this, we can find the total of the six numbers:

\[ \text{Total} = \text{Average} \times \text{Number of items} = 20 \times 6 = 120 \]

### Step 2: Calculate the total after removing one number
When one number is removed, the average of the remaining five numbers becomes 15. We can calculate the total of these five numbers:

\[ \text{Total of 5 numbers} = \text{Average} \times \text{Number of items} = 15 \times 5 = 75 \]

### Step 3: Find the number that was removed
To find the number that was removed, we can subtract the total of the five numbers from the total of the six numbers:

\[ \text{Number removed} = \text{Total of 6 numbers} - \text{Total of 5 numbers} = 120 - 75 = 45 \]

### Final Answer
The number that was removed is **45**.

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