How much money can I save on gas by losing weight? I read somewhere that if you carried around a penny in your car, over the lifetime of the car, you would end up paying an extra penny in gas than if you weren't carrying that penny.
I was wondering if a person lost say 20kg how much would they expect to save on gas?
I'm not sure what information is needed so I'll list what I think, ask me if something else is needed:


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*Person's weight = 100kg (before), 80kg (after)

*Car's average efficiency = 8 litres / 100km

*Car's unladen weight = 1185kg

*Car's average velocity = 42km/h

 A: This is a surprisingly difficult question to answer properly, but if you read the report from the Ricardo group (thanks @pentane for the reference!) it includes the following table:

They do a lot of analysis to show that if you reduce the weight of a car, you can get away with a smaller (more efficient) engine; but I am assuming that you just want the number when you are still driving the same car.
The analysis that is most useful in that case is the "fuel economy benefit" column with the baseline engine: this shows a linear improvement in fuel efficiency of 2.1% for every 5% decrease in weight reduction for the entire car. Their "small car" assumed weight (including passengers) is around 3175 pounds; you seem to have a "very small car" with an unladen weight of just 1185 kg. Their "large car" (3.0 liter engine) had a smaller decrease in fuel consumption with weight - just 1.3% for every 5% weight drop.
Using the Ricardo numbers, your 20 kg weight loss is about 44 pounds, or 1.4% of the weight of the car; that would result in a fuel economy benefit of about 0.6%. Your smaller car will do slightly better - both because the fractional weight change is greater, and because the weight effect is probably larger (just as it was smaller for the bigger car).  20 kg out of 1285 kg is 1.7% of the total weight; we might assume a fuel economy benefit of 0.7% or greater.
Translating that back to your numbers, if you are getting 8 liters per 100 km today, and you drive 15,000 km per year (1200 liters), you would save about 10 liters per year.
How much money that saves depends on where you live. I wasn't able to deduce this from either your profile or your question - but since you are using metric quantities I am going to assume "not the US". According to this list, the cheapest gas prices in the world are in Kuwait (22 US cents per liter), the most expensive, Hong Kong (\$1.85 per liter). So you stand to gain anywhere from \$2 to \$20 per year, depending on where you live. Translate that to your favorite currency.
A: Your car consumes gas because of rolling resistance and air resistance. The first one scales with the total weight (at least approximately), the second one mainly with velocity squared. Furthermore, you accelerate with the car, and this energy consumption also scales with the weight.
The amount of weight you save is $20/1285=1.6\%$. So the amount of money you can save by reducing your weight would be somewhere between $0-1.6\%$, which would depend on your average velocity.
The best way to bring down the energy consumption of your car, is to improve your driving style: no aggresive driving, anticipation to prevent a lot of braking and drive slower (less air resistance)
