I live in India and here eating biscuit after dipping it in water is a famous habit. On careful observation my classmate and me found that a sweet biscuit melts faster than a salty one when dipped in water. I don't know which law or which experimental result is working behind it, it is possible that the result is due to different composition of sweet and salty biscuits or maybe something else. I have got my mind struck there.
The disintegration of a solid food when it comes in contact with water is due to several factors, one of which might be dissolution but "melting" is unlikely to be occurring (unless the water is significantly above room temperature). I can not answer your question, it has too many culture specific concepts which I (USA) am not familiar with. In the UK (perhaps India?) a biscuit is what we call a cookie. The compositions of most cookies (in the USA) are not "biscuit-like". Even in India, I imagine, there is probably broad differences in the composition of a biscuit from cook to cook and from region to region. There are also probably significant differences in the processing. Wheat flour (only type I have some familiarity with, sorry) can be kneaded so that semi-crystalline polymers become stretched out and increase the materials toughness and strength. Baking temperatures and times also obviously will affect the final consistency (and composition: dehydration is usually a major process during baking, too little and the material has little cohesion (is gooey), too much and the material is more like a brick than a foodstuff. And I am ignoring the effects of yeast and density on the strength and cohesion of the finished biscuit. It should be obvious that a biscuit without large internal voids will be slower to absorb water. Most sugar cooky batter contains little water which leaves a large amount of very soluble sugar behind when it is baked off. Sugar is very soluble and is structurally weak, (unless caramelized). Salt, while also very water soluble and not very strong, need only be present in small quantities to give a cookie a very salty taste. If little sugar and salt is present, then the flour (which is generally not water soluble) will be slow to disintegrate.