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Difficulty: HardTables and Data Grids

The table below presents the operational performance and energy distribution metrics of four regional power grids during FY 2025–26. Net available energy for distribution is determined by first deducting transmission and storage losses from total generation, and then subtracting auxiliary station consumption.

Regional GridTotal Energy Generated (GWh)Transmission & Storage Loss (%)Auxiliary Station Consumption (GWh)Commercial Sector Share of Net Available Energy (%)
Northern Grid12,00015%20040%
Southern Grid15,00012%40035%
Eastern Grid10,00020%30050%
Western Grid18,00010%20025%

Based on the data provided, what is the ratio of the total energy distributed to the commercial sector by the Southern Grid to the combined energy distributed to the commercial sector by the Northern and Western Grids?

  1. 14 : 25Answer
  2. B
    97 : 178
  3. C
    154 : 271
  4. D
    21 : 40

Answer

The ratio of energy distributed to the commercial sector by the Southern Grid to the combined commercial distribution of the Northern and Western Grids is 14 : 25.
The correct option stating '14 : 25' accurately follows the prescribed two-stage deduction process. For the Southern Grid, subtracting 12% loss (1,800 GWh1,800\text{ GWh}) from 15,000 GWh15,000\text{ GWh} gives 13,200 GWh13,200\text{ GWh}, and subtracting 400 GWh400\text{ GWh} auxiliary consumption leaves 12,800 GWh12,800\text{ GWh}. Applying 35%35\% yields 4,480 GWh4,480\text{ GWh}. For the Northern Grid, net energy is (12,000−1,800)−200=10,000 GWh(12,000 - 1,800) - 200 = 10,000\text{ GWh}, giving 40%×10,000=4,000 GWh40\% \times 10,000 = 4,000\text{ GWh}. For the Western Grid, net energy is (18,000−1,800)−200=16,000 GWh(18,000 - 1,800) - 200 = 16,000\text{ GWh}, giving 25%×16,000=4,000 GWh25\% \times 16,000 = 4,000\text{ GWh}. Combining Northern and Western gives 8,000 GWh8,000\text{ GWh}. The ratio 4,4808,000\frac{4,480}{8,000} simplifies precisely to 14:2514 : 25.

Step-by-Step Solution

1
Calculate the net available energy and commercial distribution for the Southern Grid.
Net Available = (15,000−0.12×15,000)−400=(15,000−1,800)−400=12,800 GWh(15,000 - 0.12 \times 15,000) - 400 = (15,000 - 1,800) - 400 = 12,800\text{ GWh}. Commercial Distribution = 35% of 12,800=4,480 GWh35\% \text{ of } 12,800 = 4,480\text{ GWh}.
Transmission loss must be deducted from total generation first, followed by auxiliary consumption.
2
Calculate the net available energy and commercial distribution for the Northern Grid.
Net Available = (12,000−0.15×12,000)−200=(12,000−1,800)−200=10,000 GWh(12,000 - 0.15 \times 12,000) - 200 = (12,000 - 1,800) - 200 = 10,000\text{ GWh}. Commercial Distribution = 40% of 10,000=4,000 GWh40\% \text{ of } 10,000 = 4,000\text{ GWh}.
Required to compute the combined baseline for Northern and Western grids.
3
Calculate the net available energy and commercial distribution for the Western Grid.
Net Available = (18,000−0.10×18,000)−200=(18,000−1,800)−200=16,000 GWh(18,000 - 0.10 \times 18,000) - 200 = (18,000 - 1,800) - 200 = 16,000\text{ GWh}. Commercial Distribution = 25% of 16,000=4,000 GWh25\% \text{ of } 16,000 = 4,000\text{ GWh}.
Required to complete the denominator sum of the target ratio.
4
Compute the target ratio of Southern Grid commercial distribution to Northern + Western Grid commercial distribution.
Combined Northern + Western = 4,000+4,000=8,000 GWh4,000 + 4,000 = 8,000\text{ GWh}. Ratio = 4,480:8,000=14:254,480 : 8,000 = 14 : 25.
Simplifying 4,4808,000\frac{4,480}{8,000} by dividing both terms by their greatest common divisor 160160 yields 14:2514 : 25.

Key Concept

Multi-step tabular data interpretation involving sequential percentage reduction, absolute deductions, and ratio simplification.
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Topics

Tables and Data Grids

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