Camel and Banana, Math Puzzles

Lukas have a banana plantation and a camel. He wants to transport his 3000 bananas to the market, which is located after 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 Lucas can deliver at the market?

Answers : Math Puzzles and Riddles

      The camel can carry at most 1000 bananas and there are 3000 bananas to be carried.
      Let consider that five trips are needed to carry all the bananas from the plantation P to the place X. The place X is not the market. As the camel eats a banana for each kilometer it travels, so that it cannot travel more than 500 kilometer. Therefore the place X lies between the plantation and the market. After bringing all the bananas to the place X, consider another place Y which takes less than five trips, from X to Y. After reaching the place Y, it will take one trip to the market M.
      As an assumption one kilometer on the place PX needs 5 bananas, the one kilometer on the place XY needs 3 bananas and the one kilometer on the place YM needs 1 banana. So the distance of PX is less than the distance XY and that the distance of XY is less than the YM.
      The camel should carry exactly 2000 bananas from the place X. So we can calculate the distance of PX as 3000 - 5 x PX = 2000, therefore PX = 200 kilometers. Calculate as such for the distance XY, 2000 - 3 x XY = 1000, so XY = 333 1/3. As the both distances are less than 500, the camel can travel back from X to P and Y to X. Therefore the distance BM will be 1000 - 200 - 333 1/3 = 466 2/3.
      Now lets start from the first. Initially the camel take 1000 bananas from the plantation P to the place X at a distance of 200 kilometers. Drops 600 bananas and takes 200 bananas. Then it takes 1000 bananas from P to X and drops 600 bananas, taking 200 bananas. At last it takes 1000 bananas to the place X and drops 800 bananas. There are 2000 bananas at the place X.
      Now the travel from the place X to Y, which is 333 1/3 kilometers. First it takes 1000 bananas from X to Y, drops 333 1/3 and takes 333 1/3 to X. At last it takes 1000 bananas from X and drops 666 2/3. Totally the place Y will have 1000 bananas.
      The final voyage to the market M from Y, where the distance is 466 2/3. It takes 1000 bananas and reach the market with 533 1/3 bananas.

Solution : 533 1/3 bananas.

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