Mr Santos compares two energy tariffs, each covering the same £120 monthly usage cost. Tariff A has a fixed fee of £45 plus the usage cost adjusted by a dis...
Question 1 Report
Mr Santos compares two energy tariffs, each covering the same £120 monthly usage cost. Tariff A has a fixed fee of £45 plus the usage cost adjusted by a discount rate. Tariff B has no fixed fee, but the usage cost is increased by a surcharge rate, shown below.
- Work out the total monthly cost under Tariff A. (2)
- Work out the total monthly cost under Tariff B. (2)
- Work out the percentage by which Tariff A is more expensive than Tariff B, correct to 1 decimal place. (1)
- Next month, Mr Santos expects his usage cost to rise to £150. State, giving a reason, which tariff would then be cheaper. (1)
Answer Details
The diagram shows two labelled bars, one marked "8%" for Tariff A and one marked "22%" for Tariff B; these are the discount rate and surcharge rate referred to in the question, read directly from the figure.
(a) Tariff A applies an 8% discount to the £120 usage cost, then adds the £45 fixed fee:
\[120 \times 0.92 = \pounds 110.40\] [1 mark]
\[45 + 110.40 = \pounds 155.40\] [1 mark]
(b) Tariff B applies a 22% surcharge to the same £120 usage cost, with no fixed fee:
\[120 \times 1.22\] [1 mark]
\[= \pounds 146.40\] [1 mark]
(c) Tariff A's extra cost compared with Tariff B, as a percentage of Tariff B's cost, is:
\[\frac{155.40 - 146.40}{146.40} \times 100 = 6.1\%\] (1 d.p.) [1 mark]
(d) At £150 usage, Tariff A costs \((150 \times 0.92) + 45 = \pounds 183.00\) and Tariff B costs \(150 \times 1.22 = \pounds 183.00\). The two tariffs cost exactly the same at this usage level, so neither is cheaper [1 mark]. This happens because Tariff A's fixed fee makes it relatively better at low usage, while Tariff B's lack of a fixed fee makes it relatively better at high usage; £150 is the point where the two effects balance out.
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