The average height of the 12 students in a class is 110 cm. If 18 more students with an average height of 115 cm join the class, what will be the new average height be ?

Options

A. (a) 92 cm
B. (b) 95 cm
C. (c) 102 cm
D. (d) 113 cm

Answer

To find the new average height after additional students join the class, we can follow these steps:

### Step 1: Calculate the total height of the initial 12 students.
The average height of the 12 students is given as 110 cm.
To find the total height, we use the formula:
\[ \text{Total Height} = \text{Average Height} \times \text{Number of Students} \]
So, the total height of the 12 students is:
\[ \text{Total Height} = 110 \, \text{cm} \times 12 = 1320 \, \text{cm} \]

### Step 2: Calculate the total height of the 18 new students.
The average height of the 18 new students is given as 115 cm.
Using the same formula:
\[ \text{Total Height of New Students} = 115 \, \text{cm} \times 18 = 2070 \, \text{cm} \]

### Step 3: Calculate the combined total height of all students.
Now, we add the total heights of the initial 12 students and the 18 new students:
\[ \text{Combined Total Height} = 1320 \, \text{cm} + 2070 \, \text{cm} = 3390 \, \text{cm} \]

### Step 4: Calculate the total number of students.
The total number of students after the new students join is:
\[ \text{Total Students} = 12 + 18 = 30 \]

### Step 5: Calculate the new average height.
Finally, we can find the new average height using the formula:
\[ \text{New Average Height} = \frac{\text{Combined Total Height}}{\text{Total Students}} = \frac{3390 \, \text{cm}}{30} \]
Calculating this gives:
\[ \text{New Average Height} = 113 \, \text{cm} \]

### Final Answer:
The new average height of the class will be **113 cm**.

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