Average age of a group of five students is 14 yr. If a new student also admitted the group, new average age becomes 13 yr. Find the age of new student.

Options

A. 13yr
B. 10 yr
C. 7 yr
D. 8 yr

Answer

To solve the problem, we need to find the age of the new student based on the average ages provided. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the total age of the original group of students.
The average age of the original group of five students is 14 years. To find the total age of these students, we can use the formula for average:

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

Rearranging this gives us:

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

Substituting in the values:

\[ \text{Total Age of 5 students} = 14 \times 5 = 70 \text{ years} \]

### Step 2: Calculate the total age of the group after the new student joins.
After the new student joins, the average age of the group becomes 13 years, and now there are 6 students in total. We can again use the average formula:

\[ \text{Total Age of 6 students} = \text{Average} \times \text{Number of Students} \]

Substituting in the values:

\[ \text{Total Age of 6 students} = 13 \times 6 = 78 \text{ years} \]

### Step 3: Find the age of the new student.
To find the age of the new student, we can subtract the total age of the original group from the total age of the new group:

\[ \text{Age of new student} = \text{Total Age of 6 students} - \text{Total Age of 5 students} \]

Substituting in the values:

\[ \text{Age of new student} = 78 - 70 = 8 \text{ years} \]

### Conclusion:
The age of the new student is **8 years**.

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