2013 AIME II Problem 3

A large candle is 119 centimeters tall. It is designed to burn down more quickly when it is first lit and more slowly as it approaches its bottom. Specifically, the candle takes 10 seconds to burn down the first centimeter from the top, 20 seconds to burn down the second centimeter, and 10 k seconds to burn down the k-th centimeter. Suppose it takes T seconds for the candle to burn down completely. Then \frac{T}{2} seconds after it is lit, the candle’s height in centimeters will be h. Find 10 h.