The maximum 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 follow these steps:

### Step 1: Calculate the volume of the smaller box
The dimensions of the smaller box are:
- Length (l) = 2 m
- Breadth (b) = 4 m
- Height (h) = 5 m

The volume \( V \) of the smaller box can be calculated using the formula:
\[ V = l \times b \times h \]
Substituting the values:
\[ V = 2 \times 4 \times 5 = 40 \, \text{m}^3 \]

### Step 2: Calculate the volume of the larger box
The dimensions of the larger box are:
- Length (L) = 20 m
- Breadth (B) = 10 m
- Height (H) = 5 m

The volume \( V \) of the larger box can be calculated using the same formula:
\[ V = L \times B \times H \]
Substituting the values:
\[ V = 20 \times 10 \times 5 = 1000 \, \text{m}^3 \]

### Step 3: Determine the maximum number of smaller boxes that can fit into the larger box
To find the maximum number of smaller boxes that can fit into the larger box, we will divide the volume of the larger box by the volume of the smaller box:
\[ \text{Number of boxes} = \frac{\text{Volume of larger box}}{\text{Volume of smaller box}} = \frac{1000}{40} \]
Calculating this gives:
\[ \text{Number of boxes} = 25 \]

### Conclusion
The maximum number of boxes that can be placed in the larger box is **25**.

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