Given below in the information about solar plants installed in four
differnet colonies W,X, Y, Z . Number of solar plants in colonies W,
X, Y, Z are 24, 20, 15 and 12 respectively. Number of electricity
units produced in one week by one solar plant when they operate
with maximum efficiency in colonies W, X,Y,Z are 2 lakh units /
week , 80000 units/week , 1 Lakh units/week and 1.5 Lakh units/
week respectively. Number of houses in each colony W,X,Y,Z
are 540 , 240 , 150 and 350 respectively . total units produced are
consumed equally by each house in the colony. `to` Different number of solar plants are operated in four different weeks
In first week number of solar plants are operative in colonies W, X,Y, Z are 76`%`, 50`%`,40`%` and 75`%` respectively . In second week
it is 50`%` , 76`%`, 60`%` and 50`%` respectively. In third week it is 75`%`,
100`%` , 80`%` and 50`%` respectively. In fourth week it is 100`%`, 50`%`
60`%` and 75`%` respectively.
` to` Given below is the three ranges of efficiency of a solar plants
(numer of unit produced /week by one plant)
`{:("Efficiency Type","Range"),("Efficiency1",60%-70%),("Efficiency2",45%-55%),("Efficiency3",30%-40%):}`
`to` level 1 : Consider upper limit of range of efficiency
`to` level 2 : Consider mid of range of efficiency
`to` level 3 : Consider the lower range of efficiency
Eg If a solar plants is operative at efficiency 2 than its level 2
efficiency will ve `= (45+55)/(2)=50%`
Its level 1 efficiency will be 55`%`
lts level 3 efficiency will ve 45`%`
What is the ratio of total production of colony W in first week
at level 1 of efficiency 2 to the total production of colony X
in second week at Leval 2 of efficiency 1 .

Options

A. ` 20 : 13 `
B. `33 : 13`
C. `33. 19`
D. `27 : 19`

Explanation

To solve the problem, we need to calculate the total production of colony W in the first week at level 1 of efficiency 2 and the total production of colony X in the second week at level 2 of efficiency 1. Finally, we will find the ratio of these two productions.

### Step 1: Calculate the total production of colony W in the first week at level 1 of efficiency 2.

1. **Identify the number of solar plants in colony W**:
- Colony W has 24 solar plants.

2. **Identify the maximum efficiency production per plant**:
- Each solar plant in colony W produces 2 lakh units/week at maximum efficiency.

3. **Determine the percentage of solar plants operating in the first week**:
- In the first week, 76% of the solar plants are operational.

4. **Calculate the effective number of solar plants operating**:
- Effective solar plants = 24 * 76% = 24 * 0.76 = 18.24 (approximately 18 plants, but we will use the exact value for calculation).

5. **Determine the level 1 efficiency of efficiency 2**:
- Efficiency 2 has a range of 45% to 55%. The upper limit (level 1) is 55%.

6. **Calculate the total production for colony W**:
\[ \text{Total Production W} = \text{Number of plants} \times \text{Production per plant} \times \text{Operating percentage} \times \text{Efficiency} \]
\[ \text{Total Production W} = 24 \times 2,00,000 \times 0.76 \times 0.55 \]
\[ = 24 \times 2,00,000 \times 0.76 \times 0.55 = 24 \times 2,00,000 \times 0.418 = 20,03,200 \text{ units} \]

### Step 2: Calculate the total production of colony X in the second week at level 2 of efficiency 1.

1. **Identify the number of solar plants in colony X**:
- Colony X has 20 solar plants.

2. **Identify the maximum efficiency production per plant**:
- Each solar plant in colony X produces 80,000 units/week at maximum efficiency.

3. **Determine the percentage of solar plants operating in the second week**:
- In the second week, 76% of the solar plants are operational.

4. **Calculate the effective number of solar plants operating**:
- Effective solar plants = 20 * 76% = 20 * 0.76 = 15.2 (approximately 15 plants, but we will use the exact value for calculation).

5. **Determine the level 2 efficiency of efficiency 1**:
- Efficiency 1 has a range of 60% to 70%. The mid-range (level 2) is (60 + 70) / 2 = 65%.

6. **Calculate the total production for colony X**:
\[ \text{Total Production X} = \text{Number of plants} \times \text{Production per plant} \times \text{Operating percentage} \times \text{Efficiency} \]
\[ \text{Total Production X} = 20 \times 80,000 \times 0.76 \times 0.65 \]
\[ = 20 \times 80,000 \times 0.76 \times 0.65 = 20 \times 80,000 \times 0.494 = 7,904,000 \text{ units} \]

### Step 3: Calculate the ratio of total production of colony W to colony X.

1. **Ratio**:
\[ \text{Ratio} = \frac{\text{Total Production W}}{\text{Total Production X}} = \frac{20,03,200}{7,904,000} \]
\[ = \frac{2003200}{7904000} = \frac{20032}{79040} \approx \frac{1}{3.93} \approx 1:4 \]

### Final Answer:
The ratio of total production of colony W in the first week at level 1 of efficiency 2 to the total production of colony X in the second week at level 2 of efficiency 1 is approximately **1:4**.

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