The average age of 16 students in a college is 20. Out of them, the average age of 5 students is 20 and the average age of the other 10 students is 20.4. Find the age of the 16th college student.

Options

A. 24
B. 16
C. 20
D. 22

Answer

To find the age of the 16th college student, we can follow these steps:

### Step 1: Calculate the total age of all 16 students
The average age of 16 students is given as 20. To find the total age, we use the formula:
\[ \text{Total Age} = \text{Average Age} \times \text{Number of Students} \]
So, the total age of 16 students is:
\[ \text{Total Age} = 20 \times 16 = 320 \]

### Step 2: Calculate the total age of the first 5 students
The average age of the first 5 students is given as 20. Using the same formula:
\[ \text{Total Age of 5 Students} = 20 \times 5 = 100 \]

### Step 3: Calculate the total age of the next 10 students
The average age of the next 10 students is given as 20.4. Therefore:
\[ \text{Total Age of 10 Students} = 20.4 \times 10 = 204 \]

### Step 4: Calculate the total age of the first 15 students
Now, we can find the total age of the first 15 students by adding the total ages of the first 5 and the next 10 students:
\[ \text{Total Age of 15 Students} = \text{Total Age of 5 Students} + \text{Total Age of 10 Students} \]
\[ \text{Total Age of 15 Students} = 100 + 204 = 304 \]

### Step 5: Calculate the age of the 16th student
To find the age of the 16th student, we subtract the total age of the first 15 students from the total age of all 16 students:
\[ \text{Age of 16th Student} = \text{Total Age of 16 Students} - \text{Total Age of 15 Students} \]
\[ \text{Age of 16th Student} = 320 - 304 = 16 \]

Thus, the age of the 16th college student is **16**.