A claim about fuel
Testing somebody else's conclusion against the figures it was drawn from.
Notes and data
A delivery firm replaced eight of its forty vans with electric models in 2023 and published this summary:
Fuel and charging costs, whole fleet: £96,000 in 2022, £81,600 in 2023 Distance driven, whole fleet: 640,000 km in 2022, 512,000 km in 2023
The firm's statement reads: "Switching to electric cut our fuel bill by 15 percent."
Answers in order, explanations withheld, and a report on where the chain broke.
- 10.1Percent changeFoundation
By what percentage did the total fuel and charging bill fall?
- A15%
- B20%
- C18%
- D12%
Show the answer and reasoningHide the reasoning
15%
The fall is 96,000 - 81,600 = £14,400. Divided by the 2022 figure: 14,400 / 96,000 = 0.15, which is 15 percent. The firm's arithmetic is right.
- 10.2Percent changeStandard
Builds on: Question 1 established that the bill fell 15 percent; this asks whether anything else fell at the same time.
By what percentage did the distance driven fall?
- A20%
- B15%
- C25%
- D12.5%
Show the answer and reasoningHide the reasoning
20%
The fall is 640,000 - 512,000 = 128,000 km, and 128,000 / 640,000 = 0.20, which is 20 percent. The fleet drove considerably less as well as spending less.
- 10.3RatesChallenge
Builds on: Both earlier figures. The bill fell 15 percent while distance fell 20 percent, and a bill falling more slowly than the distance means the rate went up.
What happened to the cost per kilometre?
- AIt rose from 15p to about 15.9p.
- BIt fell from 15p to about 12.8p.
- CIt stayed at 15p.
- DIt cannot be worked out from these figures.
Show the answer and reasoningHide the reasoning
It rose from 15p to about 15.9p.
96,000 / 640,000 = £0.15 per km in 2022; 81,600 / 512,000 = £0.159 per km in 2023. The bill fell because the fleet drove less, and per kilometre it actually cost slightly more.
- 10.4Interpreting modelsChallenge
Builds on: Question 1 confirmed the arithmetic, questions 2 and 3 supplied the alternative explanation. Neither alone settles this.
Which assessment of the firm's statement is best supported?
- AThe 15 percent figure is correct, but attributing it to the switch is not supported by these figures.
- BThe 15 percent figure is wrong; the bill fell by 20 percent.
- CThe statement is fully supported by the data.
- DThe data show that electric vans cost more to run than diesel ones.
Show the answer and reasoningHide the reasoning
The 15 percent figure is correct, but attributing it to the switch is not supported by these figures.
The arithmetic holds, and the cause does not: driving 20 percent less would reduce the bill on its own. Nor do the figures show electric vans are more expensive — the fleet is mixed and the summary does not separate them.