The owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located in the desert. The distance between his banana plantation and the market is about 1000 kilometer. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.What is the largest number of bananas that can be delivered to the market?
At KM#0, we have 3000 bananas. The maximum bananas the camel can carry is 1000 so the camel must at least make 3 trips from the start point. (Leave #0, Return to #0, Leave #0, Return to #0, Leave #0).
If we move just 1km, we need 1 banana for each step mentioned above thus making a total of 5 bananas for each km.
We continue making 3 trips until we reach a banana count of 2000.
3000 – 5*d = 2000 => d = 200
At #200km, we will have 2000 bananas
At this point, we only need to make 2 trips (Leave #200, Return to #200, Leave #200). This will cost 1 banana for each step thus making a total of 3 bananas for each km.
We continue making 2 trips until we reach a banana count of 1000.
2000 – 3*d = 1000 => d = 333km
At#(200+333) = #534km, we will have 998 bananas
At this point, we need to make one trip to the camel just carries everything and marches toward the market.
Remaining km = 1000 – 534 = 466km. Bananas needed = 466.
Therefore, the bananas remaining once the camel reaches the market is 998 – 466 = 532 bananas.