Out of 20 boys, 6 are each of 1 m 15 cm height. 8 are of 1 m 10 cm and rest of 1 m 12 cm. The average height of all of them is

Options

A. 1 m 12.1 cm
B. 1 m 21.1 cm
C. 1 m 21 cm
D. 1 m 12 cm

Answer

To find the average height of the 20 boys, we will follow these steps:

### Step 1: Convert heights to centimeters
We need to convert all heights into centimeters for consistency:
- 1 m 15 cm = 100 cm + 15 cm = **115 cm**
- 1 m 10 cm = 100 cm + 10 cm = **110 cm**
- 1 m 12 cm = 100 cm + 12 cm = **112 cm**

### Step 2: Determine the number of boys at each height
- There are **6 boys** with a height of **115 cm**.
- There are **8 boys** with a height of **110 cm**.
- The remaining boys will be \( 20 - 6 - 8 = 6 \) boys with a height of **112 cm**.

### Step 3: Calculate the total height for each group
Now, we calculate the total height contributed by each group:
- Total height from 6 boys at 115 cm:
\[ 6 \times 115 = 690 \text{ cm} \]
- Total height from 8 boys at 110 cm:
\[ 8 \times 110 = 880 \text{ cm} \]
- Total height from 6 boys at 112 cm:
\[ 6 \times 112 = 672 \text{ cm} \]

### Step 4: Calculate the overall total height
Now, we sum up all the total heights calculated:
\[ \text{Total height} = 690 + 880 + 672 = 2242 \text{ cm} \]

### Step 5: Calculate the average height
To find the average height, we divide the total height by the number of boys:
\[ \text{Average height} = \frac{2242 \text{ cm}}{20} = 112.1 \text{ cm} \]

### Step 6: Convert the average height back to meters and centimeters
To express the average height in meters and centimeters:
- 112.1 cm = 1 m + 12.1 cm

### Final Answer
The average height of all the boys is **1 m 12.1 cm**.

---