Length of Tourist Visa (L type)

I am a US citizen, considering accepting an expat job position in India. While there I would like to go see the Great Wall of China. So I have to questions - how long does an L type last? I'm afraid if I got it in the US before I moved to India, the L type to visit China would expire before I had the chance to go. So if this is the case, as a US citizen in India, how/where would I apply for it to visit China?