Choosing a Power Connection for the Annexe
The annexe that houses the survey equipment needs its own electricity connection, and the estate section has two tariffs to choose from. The annexe's average consumption is 1,850 units a month, but it falls to about 600 units in the two lean months of the monsoon. Tariff D (domestic-type) charges a fixed ₹150 a month and energy at ₹4.50 a unit for the first 200 units, ₹6.00 a unit for units 201 to 500, and ₹7.50 a unit for everything above 500. Tariff C (commercial) charges a fixed ₹600 a month and a flat ₹5.60 a unit with no slabs. Meter change and wiring work cost the same under both tariffs and can be ignored. The officer asks for a recommendation with numbers, and adds a caution: the connection will run for at least three years, so a tariff that wins on the average month but loses badly in the lean months must be pointed out rather than hidden.
1. Compute the monthly bill under both tariffs at the average consumption of 1,850 units.
Read the worked answer
Tariff D (slab-wise).
- First 200 units: 200 × ₹4.50 = ₹900
- Units 201–500 (300 units): 300 × ₹6.00 = ₹1,800
- Above 500 (1,850 − 500 = 1,350 units): 1,350 × ₹7.50 = ₹10,125
- Energy charge = 900 + 1,800 + 10,125 = ₹12,825
- Add fixed charge: 12,825 + 150 = ₹12,975
Tariff C (flat).
- Energy: 1,850 × ₹5.60 = ₹10,360
- Add fixed charge: 10,360 + 600 = ₹10,960
At the average month, Tariff C is cheaper by ₹12,975 − ₹10,960 = ₹2,015.
The slab structure is what decides this: at 1,850 units, 1,350 units are billed at the top rate of ₹7.50, which pulls the effective rate for D up to about ₹7.01 a unit, far above C's flat ₹5.60.
2. Find the monthly consumption at which the two tariffs cost the same, and explain how that figure should be used in the recommendation.
Read the worked answer
For any consumption above 500 units, Tariff D costs: 150 + 900 + 1,800 + 7.50(x − 500) = 2,850 + 7.50x − 3,750 = 7.50x − 900. Tariff C costs: 600 + 5.60x.
Set them equal: 7.50x − 900 = 5.60x + 600 1.90x = 1,500 x = 789.47, i.e. about 790 units a month.
Check: at x = 790, D = 7.50(790) − 900 = ₹5,025; C = 600 + 5.60(790) = ₹5,024. The two agree to within a rupee.
How to use it: 790 units is the crossover. Below it, the low fixed charge makes D cheaper; above it, C's flat rate wins. Since the annexe averages 1,850 units, it sits far to the right of the crossover, so the choice is not close in the normal month. The crossover figure is useful mainly to show that the decision is robust - consumption would have to fall by more than half before the recommendation changed.
3. Now take the lean months into account and give the final recommendation for a full year, with the reasoning exposed.
Read the worked answer
Lean month at 600 units.
- Tariff D: 150 + 900 + 1,800 + (100 × 7.50 = 750) = ₹3,600
- Tariff C: 600 + (600 × 5.60 = 3,360) = ₹3,960
- D is cheaper by ₹360 in each lean month.
Full year (10 average months + 2 lean months).
- Tariff D: (12,975 × 10) + (3,600 × 2) = 129,750 + 7,200 = ₹1,36,950
- Tariff C: (10,960 × 10) + (3,960 × 2) = 109,600 + 7,920 = ₹1,17,520
Recommendation: Tariff C, cheaper by ₹19,430 a year.
The officer's caution is met by showing the loss explicitly rather than hiding it: D saves ₹720 a year across the two lean months, but C saves ₹20,150 across the ten average months, so the net advantage of C is ₹19,430. Because the connection will run for three years, the decision should not be reversed by a single unusual month; only a sustained drop below roughly 790 units a month would justify reopening it.