Answer:
Paper in a warm moist landfill will decompose in 2 or 3 weeks. If it is cooler and drier, then it will take longer. Paper will survive in a very dry climate for many hundreds of years (people find old newspapers in the walls of their houses).
Stronger paper, like cartridge paper and board will take longer, depending on the thickness and toughness, as well as the moisture and heat mentioned above.