BahnCard 25 / 50 / 100 Question

Question

Hi guys,

the following interview question came up recently:

BahnCard 25 costs 50 €
BahnCard 50 costs 200 €
BahnCard 100 costs 3000 €

(for international prepers: BahnCard is a loyalty card of the german railroad company that costs the stated amount and provides a discount which is given in the name)

1. How many kilometers do you have to travel to break even with each BahnCard (easy and solved)

2. From how many kilometers on exactly is BahnCard 100 the better choice?

To make it easy the interviewer assumed that 1km costs 1 €.

Thank you very much :)

Answer 1

Hello!

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Answer 2

Answer should be 5600km.

1. Find total kms where: Avg. BC25 = BC100 (50 + x*0.75)/x = 3000/x

2. Find total kms where: Avg. BC50 = BC100 (200 + x*0.50)/x = 3000/x

The larger answer is the correct one.

Hint:

At ≈4000km BC100 would have a lower Avg. (cost / km) than BC25

At ≈5600km BC100 would have a lower Avg. (cost / km) than BC50

Anything beyond 5600km, BC100 would cost nothing, but BC50 would still carry an additional charge of €0.50/km.

Answer 3

Hello!

To determine from how many kilometers on the BahnCard 100 becomes the better choice, we need to compare the total cost of traveling with the BahnCard 100 to the cost of traveling without any BahnCard. Let's calculate it:

Cost of traveling with BahnCard 100 = 3000 €
Cost of traveling without any BahnCard = Total distance (in kilometers) * Cost per kilometer (1 €)

To find the breakeven point, we set these two costs equal to each other and solve for the total distance:

3000 € = Total distance * 1 €

Simplifying the equation:

Total distance = 3000 € / 1 €
Total distance = 3000 kilometers

Therefore, if you plan to travel more than 3000 kilometers in total, the BahnCard 100 becomes the better choice compared to traveling without any BahnCard.