## Thursday, 12 July 2012

### Camel and Grass

Consider a camel who needs to transport 3000 kg of grass to a city 1000 km far. However, camel can only load 1000kg in one go. Also for every km he walks, he eats a kg of grass. Find the maximum possible amount of grass that can be transported.

1. you can do 666.

take 3 loads of 1000 each to a distance of 667. the camel will eat 667*3 = 2001
remaining = 999

next step: transfer the entire amount in 1 go to the end
distance = 333
camel eats 333
remaining = 666

2. @Aditya: I think you have forgotten about the grass consumption during the return journey of the camel.

The solution is:
For every 1km movement of 3000kg of grass, the camel would consume 5kg of grass initially. This is explained below:
The camel will carry 1st lot and store it at 1 km distance and return back. During this it will consume 2 kg of grass. He will do the same with the 2nd lot and consume another 2 kg. For the final lot, he would not return back, thus will consume only 1 kg.

Thus, for every 1km movement of 3000kg of grass, the camel would consume 5kg of grass initially. Also, the grass would get depleted by 5kg after every 1 km. Thus, by 200kms, the camel would be left with only 2000 kg of grass(i.e.) only 2 lots.

Thus, for every 1km movement of 2000kg of grass, the camel would consume 3kg of grass now. Also, the grass would get depleted by 3kg after every 1 km. Thus, by next 333kms(total 533kms = 200+333), the camel would be left with only 1000 kg of grass(i.e.) only 1 lot.

Now, the camel could take the entire 1 lot in one go and the remaining distance to be covered would be 1000-533= 467 km. Thus, the total grass taht the camel would consume during the trip would be 467kg.

Thus, the final amount transferred would be 1000-467 = 533kg only