Under a state renewable energy initiative, a total capacity of 15,000\text{ kW} of solar p… — State PSC Exam

Under a state renewable energy initiative, a total capacity of $15,000\text{ kW}$ of solar panels was installed across three districts: District Alpha, District Beta, and District Gamma. District Alpha was allocated $40\%$ of the total capacity. The capacity installed in District Beta was $\frac{3}{4}$ of that in District Alpha, while the remaining capacity was installed in District Gamma. In District Alpha, $60\%$ of the installed capacity consists of rooftop solar panels, and the remainder consists of ground-mounted panels. In District Beta, the ratio of rooftop solar capacity to ground-mounted solar capacity is $2 : 3$ . In District Gamma, the ground-mounted solar capacity exceeds the rooftop solar capacity by $1,500\text{ kW}$ .

Based on the provided information, which of the following statements regarding the solar panel capacity distribution are correct?

The total rooftop solar capacity installed across all three districts is $6,900\text{ kW}$ .Answer
The ground-mounted solar capacity in District Gamma is exactly twice its rooftop solar capacity.Answer
C
District Beta accounts for $35\%$ of the total solar panel capacity installed across all three districts.
The ratio of total ground-mounted solar capacity to total rooftop solar capacity across all three districts is $27 : 23$ .Answer

Answer

The statements confirming that total rooftop solar capacity is

6,900\text{ kW}

, ground-mounted capacity in District Gamma is twice its rooftop capacity, and the ratio of total ground-mounted to rooftop capacity is

27 : 23

are all correct.

Evaluating the data step by step shows that District Alpha has

3,600\text{ kW}

rooftop and

2,400\text{ kW}

ground-mounted capacity; District Beta has

1,800\text{ kW}

rooftop and

2,700\text{ kW}

ground-mounted capacity; District Gamma has

1,500\text{ kW}

rooftop and

3,000\text{ kW}

ground-mounted capacity. This confirms that total rooftop capacity is

6,900\text{ kW}

, District Gamma's ground-mounted capacity is twice its rooftop capacity (

3,000\text{ kW} = 2 \times 1,500\text{ kW}

), and the overall ratio of ground-mounted to rooftop capacity is

8,100 : 6,900 = 27 : 23

Step-by-Step Solution

Calculate total capacity allocation for each district.

Alpha =

40\% \text{ of } 15,000 = 6,000\text{ kW}

. Beta =

\frac{3}{4} \times 6,000 = 4,500\text{ kW}

. Gamma =

15,000 - (6,000 + 4,500) = 4,500\text{ kW}

Determining individual district totals is necessary to break down capacity by panel type.

Determine rooftop and ground-mounted capacities for District Alpha and District Beta.

District Alpha: Rooftop =

60\% \text{ of } 6,000 = 3,600\text{ kW}

, Ground =

2,400\text{ kW}

. District Beta: Ratio

2:3 \implies

Rooftop =

\frac{2}{5} \times 4,500 = 1,800\text{ kW}

, Ground =

\frac{3}{5} \times 4,500 = 2,700\text{ kW}

Applying given percentages and ratios yields the exact breakdown for Alpha and Beta.

Determine rooftop and ground-mounted capacities for District Gamma.

Let Rooftop =

R

and Ground =

G

. We have

G + R = 4,500

and

G - R = 1,500

. Solving gives

2G = 6,000 \implies G = 3,000\text{ kW}

and

R = 1,500\text{ kW}

Setting up simultaneous equations resolves the unknown components for Gamma.

Verify overall totals and evaluate each statement.

Total Rooftop =

3,600 + 1,800 + 1,500 = 6,900\text{ kW}

. Total Ground =

2,400 + 2,700 + 3,000 = 8,100\text{ kW}

. Gamma Ground/Rooftop ratio =

3,000 / 1,500 = 2

. Beta percentage of total =

4,500 / 15,000 = 30\%

. Ground to Rooftop ratio =

8,100 / 6,900 = 27 / 23

Direct comparison evaluates which statements are factually supported by the paragraph data.

Key Concept

Data extraction and simultaneous calculation from unstructured paragraph-based quantitative scenarios.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic