The average height of 30 boys out of a class of 50 is 160 cm. If the average height of the remaining boys is 165 cm, the average height of the whole class (in cm) is :

Options

A. 161
B. 162
C. 163
D. 164

Answer

To find the average height of the whole class, we can use the formula for the combined average of two groups. Here’s how we can solve the problem step by step:

### Step 1: Identify the number of boys in each group and their average heights.
- Group 1: 30 boys with an average height of 160 cm.
- Group 2: 20 boys (since there are 50 boys in total) with an average height of 165 cm.

### Step 2: Calculate the total height of boys in each group.
- For Group 1:
\[ \text{Total height of Group 1} = \text{Number of boys} \times \text{Average height} = 30 \times 160 = 4800 \text{ cm} \]

- For Group 2:
\[ \text{Total height of Group 2} = \text{Number of boys} \times \text{Average height} = 20 \times 165 = 3300 \text{ cm} \]

### Step 3: Calculate the total height of the whole class.
\[ \text{Total height of the whole class} = \text{Total height of Group 1} + \text{Total height of Group 2} = 4800 + 3300 = 8100 \text{ cm} \]

### Step 4: Calculate the average height of the whole class.
\[ \text{Average height of the whole class} = \frac{\text{Total height of the whole class}}{\text{Total number of boys}} = \frac{8100}{50} = 162 \text{ cm} \]

### Final Answer:
The average height of the whole class is **162 cm**.

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