The average age of a' family with 5 members is 28 years. If one of the members of age 20 years is excluded, the average age of the family becomes

Options

A. 25 years
B. 20 years
C. 30 years
D. 24 years

Answer

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

### Step 1: Calculate the total age of the family
Given that the average age of the family with 5 members is 28 years, we can calculate the total age of the family using the formula for average:

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

Rearranging this gives us:

\[ \text{Total Age} = \text{Average} \times \text{Number of Members} \]

Substituting the given values:

\[ \text{Total Age} = 28 \times 5 = 140 \text{ years} \]

### Step 2: Exclude the age of the member
Now, we need to exclude the age of the member who is 20 years old from the total age calculated:

\[ \text{New Total Age} = \text{Total Age} - \text{Age of Excluded Member} \]

Substituting the values:

\[ \text{New Total Age} = 140 - 20 = 120 \text{ years} \]

### Step 3: Calculate the new average age
After excluding one member, the number of remaining members is 4. We can now calculate the new average age:

\[ \text{New Average} = \frac{\text{New Total Age}}{\text{Number of Remaining Members}} \]

Substituting the values:

\[ \text{New Average} = \frac{120}{4} = 30 \text{ years} \]

### Final Answer
The new average age of the family after excluding the member who is 20 years old is **30 years**.

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