The premises of a bank are to be renovated. The renovation is in terms of looring. Certain areas are to be floored either with marble or wood. All reooms/hals and pantry are rectangular. The area to be renovated comprises of a hall for customer transaction measuring 23 m by 29m, branch manager's room measurng 13m, by 71, a pantry measuring 14m by 13m, a record keeping cum server room measuring 21 m by 13m and area measruing 29 m by 21m. Total area of the bank is 2000 squae meters. The cost of wooden flooring is Rs. 170/-per squae meter and the cost of marble flooring is Rs. 190/-per square meter. The locker area, record keeping cum server room and pantry are to be floored with marble. The branch manager's room and the hall for customer transaction are to be floored with wood. No other area is to be renovated in terms of flooring.
What is the respective ratio of the total cost of wooden flooring to the total cost of marble flooring ?

Explanation

To solve the problem, we need to calculate the total costs of wooden and marble flooring based on the areas provided, and then find the respective ratio of these costs.

### Step 1: Calculate the area of each room
1. **Hall for customer transaction**:
\[ \text{Area} = 23 \, \text{m} \times 29 \, \text{m} = 667 \, \text{m}^2 \]

2. **Branch manager's room**:
\[ \text{Area} = 13 \, \text{m} \times 17 \, \text{m} = 221 \, \text{m}^2 \]

3. **Pantry**:
\[ \text{Area} = 14 \, \text{m} \times 13 \, \text{m} = 182 \, \text{m}^2 \]

4. **Record keeping cum server room**:
\[ \text{Area} = 21 \, \text{m} \times 13 \, \text{m} = 273 \, \text{m}^2 \]

5. **Locker area**:
\[ \text{Area} = 29 \, \text{m} \times 21 \, \text{m} = 609 \, \text{m}^2 \]

### Step 2: Identify areas for flooring
- **Wooden flooring**:
- Hall for customer transaction: 667 m²
- Branch manager's room: 221 m²
- **Total wooden area**:
\[ 667 + 221 = 888 \, \text{m}^2 \]

- **Marble flooring**:
- Pantry: 182 m²
- Record keeping cum server room: 273 m²
- Locker area: 609 m²
- **Total marble area**:
\[ 182 + 273 + 609 = 1064 \, \text{m}^2 \]

### Step 3: Calculate the costs
- **Cost of wooden flooring**:
\[ \text{Cost} = 888 \, \text{m}^2 \times 170 \, \text{Rs/m}^2 = 150960 \, \text{Rs} \]

- **Cost of marble flooring**:
\[ \text{Cost} = 1064 \, \text{m}^2 \times 190 \, \text{Rs/m}^2 = 201160 \, \text{Rs} \]

### Step 4: Calculate the ratio of costs
- **Ratio of total cost of wooden flooring to total cost of marble flooring**:
\[ \text{Ratio} = \frac{150960}{201160} \]

### Step 5: Simplify the ratio
1. Divide both numbers by 10:
\[ \frac{15096}{20116} \]

2. Find the GCD or simplify further:
- Both numbers can be divided by 4:
\[ \frac{3774}{5029} \]

3. Thus, the ratio is:
\[ 3774 : 5029 \]

### Final Answer
The respective ratio of the total cost of wooden flooring to the total cost of marble flooring is **3774:5029**.

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