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Abstract In this paper, we give an affirmative answer to the following question: Is the solvability of some nonlinear dynamic equations on a time scale T $\mathbb{T}$ not only sufficient but in a certain sense also necessary for the validity of some dynamic Hardy-type inequalities with two different weights? In fact, this answer will give a new characterization of the weights in a weighted Hardy-type inequality on time scales. The results contain the results when T=R $\mathbb{T}=\mathbb{R}$, T=N $\mathbb{T}=\mathbb{N}$, and when T=qN0 $\mathbb{T}=q^{\mathbb{N}_{0}}$ as special cases. Some applications are given for illustrations.