The number of planks of dimension `(4m xx 50 cm x 20 cm )`, then plank many plank can be stored in a pit which is 16m long, 12 m wide and 40 m wide is :

Options

A. 1900
B. 1920
C. 1800
D. 1840

Explanation

To find the number of planks that can be stored in a pit, we need to follow these steps:

### Step 1: Convert the dimensions of the planks to meters
The dimensions of the plank are given as:
- Length = 4 m
- Breadth = 50 cm
- Height = 20 cm

We need to convert the breadth and height from centimeters to meters.

- **Breadth in meters**:
\[ 50 \text{ cm} = 50 \times \frac{1}{100} \text{ m} = 0.5 \text{ m} \]

- **Height in meters**:
\[ 20 \text{ cm} = 20 \times \frac{1}{100} \text{ m} = 0.2 \text{ m} \]

### Step 2: Calculate the volume of the plank
The volume \( V \) of a cuboid is calculated using the formula:
\[ V = \text{Length} \times \text{Breadth} \times \text{Height} \]
For the plank:
\[ V_{\text{plank}} = 4 \text{ m} \times 0.5 \text{ m} \times 0.2 \text{ m} \]
Calculating this:
\[ V_{\text{plank}} = 4 \times 0.5 \times 0.2 = 4 \times 0.1 = 0.4 \text{ m}^3 \]

### Step 3: Calculate the dimensions of the pit
The dimensions of the pit are given as:
- Length = 16 m
- Width = 12 m
- Depth = 4 m

### Step 4: Calculate the volume of the pit
Using the same volume formula:
\[ V_{\text{pit}} = \text{Length} \times \text{Width} \times \text{Depth} \]
Calculating the volume of the pit:
\[ V_{\text{pit}} = 16 \text{ m} \times 12 \text{ m} \times 4 \text{ m} \]
Calculating this:
\[ V_{\text{pit}} = 16 \times 12 \times 4 = 768 \text{ m}^3 \]

### Step 5: Calculate the number of planks that can fit in the pit
To find the number of planks, we divide the volume of the pit by the volume of one plank:
\[ \text{Number of planks} = \frac{V_{\text{pit}}}{V_{\text{plank}}} \]
Substituting the values:
\[ \text{Number of planks} = \frac{768 \text{ m}^3}{0.4 \text{ m}^3} = 1920 \]

### Final Answer
The number of planks that can be stored in the pit is **1920**.

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