This is probably Gentian Violet. This antifungal/antibacterial dye has two other names, Crystal Violet and Methyl Violet both of which would fit the purpose here. All the same, the most likely answer is Gentian Violet.
I'm assuming the question setter was thinking of body piercings beneath clothing. I can't say I've seen many teenagers walking about with this bright purple dye colouring their ear lobes, ear helixes, noses, lips or tongues!