After asking how much money my brother gave my sister, my sister had three times more money than her brother. It is known that my sister has 320 yuan and my brother has 180 yuan, so the sum of their money remains unchanged, 320+ 180=500 yuan. When my sister's money is three times more than my brother's, if I take my brother's money as one, it will be four in total. So you can use 500÷4= 125 yuan to calculate my brother's money now.

180- 125=55 yuan

Answer: After my brother gave my sister 55 yuan. My sister has three times more money than my brother.