The length and the breadth of a conference hall are in the ratio `7:4` and its perimeter is 110m. Find:
(i) are of the floor of the hall.
(ii) number of tiles, each of rectangle of size `25 cm xx 20 cm`, required for flooring of the hall.
(iii) the cost of the tiles at the rate of Rs. 1,400 per hundred tiles.

Answer

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Determine the Length and Breadth
Given that the length (L) and breadth (B) of the conference hall are in the ratio of 7:4, we can express them as:
- Length (L) = 7x
- Breadth (B) = 4x

The perimeter (P) of a rectangle is given by the formula:
\[ P = 2(L + B) \]
Given that the perimeter is 110 m, we can set up the equation:
\[ 2(7x + 4x) = 110 \]

### Step 2: Solve for x
Simplifying the equation:
\[ 2(11x) = 110 \]
\[ 22x = 110 \]
Now, divide both sides by 22:
\[ x = \frac{110}{22} = 5 \]

### Step 3: Calculate Length and Breadth
Now that we have the value of x, we can find the length and breadth:
- Length (L) = 7x = 7 * 5 = 35 m
- Breadth (B) = 4x = 4 * 5 = 20 m

### Step 4: Calculate the Area of the Conference Hall
The area (A) of the rectangle is given by:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 35 \times 20 = 700 \, m^2 \]

### Step 5: Calculate the Number of Tiles Required
Each tile has dimensions of 25 cm x 20 cm. First, we need to convert the area of the hall from square meters to square centimeters:
\[ 1 \, m^2 = 10,000 \, cm^2 \]
So,
\[ 700 \, m^2 = 700 \times 10,000 \, cm^2 = 7,000,000 \, cm^2 \]

Now, calculate the area of one tile:
\[ \text{Area of one tile} = 25 \, cm \times 20 \, cm = 500 \, cm^2 \]

Now, we can find the number of tiles (N) required:
\[ N = \frac{\text{Total Area}}{\text{Area of one tile}} = \frac{7,000,000 \, cm^2}{500 \, cm^2} = 14,000 \]

### Step 6: Calculate the Cost of the Tiles
The cost of tiles is given as Rs. 1,400 for 100 tiles. First, find the cost of one tile:
\[ \text{Cost of one tile} = \frac{1400}{100} = 14 \, Rs \]

Now, calculate the total cost for 14,000 tiles:
\[ \text{Total Cost} = 14,000 \times 14 = 196,000 \, Rs \]

### Final Answers:
(i) Area of the floor of the hall = 700 m²
(ii) Number of tiles required = 14,000
(iii) Cost of the tiles = Rs. 196,000

---