Its because China, like India follows the lunar calendar. As a result, the two neighbours celebrate several auspicious days at the same time. Take for example, On the 27th of September, China celebrated the mid autumn festival while India celebrated the Ganesh festival. Similarly, Chinese New Year was celebrated on February 19th this year, while Maha shivratri was celebrated in India on February 17th. Also, an auspicious day in the holy month of Ramadan was June 20th, the 5th day of the 5th lunar month which coincided with the Dragon Boat Festival in China.
Both being ancient civilizations, the lunar calendar is still rooted strongly in both cultures. While India and China now follow the solar calendar for ease of use with the West, traditional holidays and festivals are maintained by the lunar calendar. Besides the behmoth neighbours, Pakistan, Korea, Japan, Vietnam and Nepal all also follow the lunar calendar. In the lunar calendar, the months begin on the day of the dark moon, and end on the day before the next dark moon. There are 29 or 30 days in a month.