In a reading club, the average age of the 30 members is 15 years. If a new member joins the group, the overall average age rises by 0.5 years. Determine the age of the new member.

The correct answer is 30.5.

To find the age of the new member, we can calculate the total age of all members before and after the new member joins.

Step 1: Calculate the total age of the initial 30 members.
The average age of the 30 members is 15 years.
$\text{Initial Total Age}=30\times 15=450\text{years}$

Step 2: Calculate the new total age after the new member joins.
When 1 new member joins, the total number of members becomes 30 + 1 = 31.
The average age rises by 0.5 years, making the new average age 15 + 0.5 = 15.5 years.
$\text{New Total Age}=31\times 15.5=480.5\text{years}$

Step 3: Find the age of the new member.
Subtract the initial total age from the new total age:
$\text{Age of New Member}=480.5-450=30.5\text{years}$

Therefore, the age of the new member is 30.5 years.