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

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total age of the initial group of students.
The average age of the group of 5 students is given as 14 years. To find the total age of these 5 students, we can use the formula:

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

Substituting the values:

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

### Step 2: Calculate the total age of the group after the new student joins.
After a new student joins, the average age of the group becomes 13 years with a total of 6 students. We can again use the formula for total age:

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

Substituting the values:

\[ \text{Total Age with New Student} = 13 \times 6 = 78 \text{ years} \]

### 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 group after the new student joined:

\[ \text{Age of New Student} = \text{Total Age with New Student} - \text{Total Age} \]

Substituting 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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