I don't know where you got these questions from, but they're written in a pretty lousy English.

Now, your rate is x percent.
At the end of the year, you get:
1500 (1 + x/100) = 1500 + 15x. This means that, for your $1500 investment, the "income" (it should say "return"), you get 15x.

If the rate turns into x + 2, you have:
1500[1 + (x+2)/100] = 1500 + 15(x+2). In this case, the return will be 15(x +2).

The problem tells you that the return comes up to $90, so 15(x + 2) = 90. This means that x+2 is 90/15 = 6, so x = 4%.