Question 42
Several white and black balls can be divided into pairs so that exactly $\frac{10}{11}$ of the white balls are in mixed pairs (with one white and one black ball), and the remaining ones are in pairs with the same color. Also the balls can be divided into pairs so that exactly $\frac{12}{13}$ of the black balls are in mixed pairs, and the remaining ones are in pairs with the same color. The number of white balls is between 150 and 200. How many balls of each color can there be?