[latex]d-number\ of\ dogs\\c-number\ of\ cats\\c:d=10:1\to\frac{c}{d}=\frac{10}{1}\\-------------------\\subtitute\ c=60:\\\\\frac{60}{d}=\frac{10}{1}\ \ \ \ \ |cross\ multiply\\\\10\cdot d=60\cdot1\\\\10d=60\ \ \ \ |divide\ both\ sdies\ by\ 10\\\\\boxed{d=6}\leftarrow answer[/latex]

so if the ratio is 10:1 so after that it would be 20:2 see the pattern after that 30:3, 40:4, 50:5 and finally 60:6