In a combined family the average age of 4 males and 7females is 42 and 20 years respectively. If two persons whose average age is 13 years have left the family and other three people joined the family whose respective ages are 11, 15 and 28 years, then the average age of the new family is increased by :

Options

A. 4 years
B. 1 years
C. 3 years
D. none of these

Answer

To solve the problem step by step, we will calculate the average age of the family before and after the changes.

### Step 1: Calculate the total age of males and females
- The average age of 4 males is 42 years.
- Total age of males = Average age × Number of males = 42 × 4 = 168 years.

- The average age of 7 females is 20 years.
- Total age of females = Average age × Number of females = 20 × 7 = 140 years.

### Step 2: Calculate the total age of the entire family
- Total age of the family = Total age of males + Total age of females = 168 + 140 = 308 years.

### Step 3: Calculate the average age of the family
- Total number of family members = 4 males + 7 females = 11 members.
- Average age of the family = Total age / Total number of family members = 308 / 11 = 28 years.

### Step 4: Calculate the total age after two persons leave
- Two persons leave with an average age of 13 years.
- Total age of the two persons who left = 13 × 2 = 26 years.
- New total age after they leave = Total age - Total age of persons who left = 308 - 26 = 282 years.

### Step 5: Calculate the total age after three new persons join
- The ages of the three new persons are 11, 15, and 28 years.
- Total age of new persons = 11 + 15 + 28 = 54 years.
- New total age after they join = New total age after leaving + Total age of new persons = 282 + 54 = 336 years.

### Step 6: Calculate the new total number of family members
- After two persons leave and three join, the new total number of family members = 11 - 2 + 3 = 12 members.

### Step 7: Calculate the new average age of the family
- New average age = New total age / New total number of family members = 336 / 12 = 28 years.

### Step 8: Calculate the increase in average age
- The average age before changes was 28 years, and after changes, it is still 28 years.
- Increase in average age = New average age - Old average age = 28 - 28 = 0 years.

### Final Answer
The average age of the new family is increased by **0 years**.

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