can some one correct me if im wrong!!
I dont think we need statements to find the reminder, question itself provide enough info..here how i solved
That is wrong on many many levels. You are lucky that this approach got you on the right answer, but that is purely by chance.
First the 2 'q's are NOT the same.
So you can write n=3q1 + 2 and t=5q2 + 3. But you cannot assume that q1=q2.
Also even if you did multiply the above as stated, you'd have (3q+2)(5q+3) = 15q^2 + 9q + 10q + 6 = 15q^2 + 19 q + 6, which is a quadratic and you have no idea whether 19 q is divisible by 15. However, you CANNOT do this at all, so this approach is incorrect.
The previous posts are really good and helpful. Study those closely. They do elaborate how to answer the question.