The maxumum number of boxes , each of length 2 m , breadth 4 m and height 5 m that can be placed in a box of length 20 m , breadth 10 m and height 5 m is

Options

A. 30
B. 40
C. 20
D. 25

Answer

To find the maximum number of smaller boxes that can fit into a larger box, we will use the formula for the volume of a cuboid. Here are the steps to solve the problem:

### Step-by-Step Solution:

1. **Identify the dimensions of the smaller box:**
- Length (l) = 2 m
- Breadth (b) = 4 m
- Height (h) = 5 m

2. **Identify the dimensions of the larger box:**
- Length (L) = 20 m
- Breadth (B) = 10 m
- Height (H) = 5 m

3. **Calculate the volume of the smaller box:**
\[ \text{Volume of smaller box} = l \times b \times h = 2 \, \text{m} \times 4 \, \text{m} \times 5 \, \text{m} = 40 \, \text{m}^3 \]

4. **Calculate the volume of the larger box:**
\[ \text{Volume of larger box} = L \times B \times H = 20 \, \text{m} \times 10 \, \text{m} \times 5 \, \text{m} = 1000 \, \text{m}^3 \]

5. **Determine the maximum number of smaller boxes that can fit into the larger box:**
\[ \text{Number of smaller boxes (m)} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{1000 \, \text{m}^3}{40 \, \text{m}^3} = 25 \]

Thus, the maximum number of smaller boxes that can be placed in the larger box is **25**.