Shanti sweets stall was placing an order for making cardboard boxes for packing their sweets. Two sizes of boxes were required. The bigger of dimensions `25cm xx 20cm xx 5 cm` and the smaller of dimensions `15cm xx 12cm xx 5cm`. For all the overlaps, `5%` of the total surface area is required for supplying `250` boxes of each kind.

Options

A. `2184`
B. `4980`
C. `1900`
D. `9100`

Explanation

To solve the problem of calculating the total surface area required for the cardboard boxes and the cost associated with them, we will follow these steps:

### Step 1: Calculate the Surface Area of the Bigger Box

The dimensions of the bigger box are \(25 \, \text{cm} \times 20 \, \text{cm} \times 5 \, \text{cm}\).

The formula for the surface area \(A\) of a rectangular box is given by:
\[ A = 2(lw + lh + wh) \]
where \(l\), \(w\), and \(h\) are the length, width, and height of the box respectively.

Substituting the values:
\[ A = 2(25 \times 20 + 25 \times 5 + 20 \times 5) \]
Calculating each term:
- \(25 \times 20 = 500\)
- \(25 \times 5 = 125\)
- \(20 \times 5 = 100\)

Now substitute these back into the formula:
\[ A = 2(500 + 125 + 100) = 2(725) = 1450 \, \text{cm}^2 \]

### Step 2: Calculate the Surface Area of the Smaller Box

The dimensions of the smaller box are \(15 \, \text{cm} \times 12 \, \text{cm} \times 5 \, \text{cm}\).

Using the same surface area formula:
\[ A = 2(15 \times 12 + 15 \times 5 + 12 \times 5) \]
Calculating each term:
- \(15 \times 12 = 180\)
- \(15 \times 5 = 75\)
- \(12 \times 5 = 60\)

Now substitute these back into the formula:
\[ A = 2(180 + 75 + 60) = 2(315) = 630 \, \text{cm}^2 \]

### Step 3: Calculate the Total Surface Area for 250 Boxes of Each Kind

For the bigger boxes:
\[ \text{Total Surface Area for Bigger Boxes} = 250 \times 1450 = 362500 \, \text{cm}^2 \]

For the smaller boxes:
\[ \text{Total Surface Area for Smaller Boxes} = 250 \times 630 = 157500 \, \text{cm}^2 \]

### Step 4: Calculate the Combined Surface Area

Now, add the surface areas of both types of boxes:
\[ \text{Total Surface Area} = 362500 + 157500 = 520000 \, \text{cm}^2 \]

### Step 5: Add 5% for Overlaps

To account for overlaps, calculate 5% of the total surface area:
\[ \text{Overlap Area} = 0.05 \times 520000 = 26000 \, \text{cm}^2 \]

Now add this to the total surface area:
\[ \text{Total Surface Area with Overlaps} = 520000 + 26000 = 546000 \, \text{cm}^2 \]

### Step 6: Calculate the Cost

The cost is given as \(4 \, \text{rupees for every 1000 cm}^2\).

First, find the total cost:
\[ \text{Cost} = \frac{546000}{1000} \times 4 = 546 \times 4 = 2184 \, \text{rupees} \]

### Final Answer
The total cost for the cardboard boxes is **2184 rupees**.

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