The average height of the students in a class of 10 is 105 cm .If 20 more students with an average height of 120 cm join the class , what will the new average height be ?

Options

A. 105 cm
B. 110 cm
C. 112 cm
D. 115 cm

Answer

To find the new average height of the students after adding more students to the class, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Total Height of the Original Students:**
- The average height of the original 10 students is 105 cm.
- To find the total height of these students, we use the formula:
\[ \text{Total Height} = \text{Average Height} \times \text{Number of Students} \]
- So, the total height of the original students is:
\[ \text{Total Height} = 105 \, \text{cm} \times 10 = 1050 \, \text{cm} \]

2. **Calculate the Total Height of the New Students:**
- The average height of the 20 new students is 120 cm.
- Again, we use the same formula to find their total height:
\[ \text{Total Height of New Students} = 120 \, \text{cm} \times 20 = 2400 \, \text{cm} \]

3. **Calculate the Combined Total Height:**
- Now, we add the total heights of the original students and the new students:
\[ \text{Combined Total Height} = 1050 \, \text{cm} + 2400 \, \text{cm} = 3450 \, \text{cm} \]

4. **Calculate the Total Number of Students:**
- The total number of students after adding the new students is:
\[ \text{Total Students} = 10 + 20 = 30 \]

5. **Calculate the New Average Height:**
- Finally, we calculate the new average height using the combined total height and the total number of students:
\[ \text{New Average Height} = \frac{\text{Combined Total Height}}{\text{Total Students}} = \frac{3450 \, \text{cm}}{30} \]
- Performing the division:
\[ \text{New Average Height} = 115 \, \text{cm} \]

### Final Answer:
The new average height of the students in the class is **115 cm**.

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