Which of the following is grammatical when giving someone something they want?
- I hope this could help you.
- I hope it can help you.
- Hoped this may help you.
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"I hope this could help you" sounds wrong. As could is past tense, and you're taking about present/future tense.
"I hope this can help you" is okay, but not very strong as you are only hoping the thing has the capability to help.
"I hope this may help you" is also okay, and is a bit stronger, as you are hoping that the thing has a likelihood, or a probability of helping.
I would also consider, "I hope this will help you", as this is the strongest, and hopes that the thing will most definitely, certainly help.