Answer: Let us assume that our income is $X.
In the first case:
1) We received a raise and our income increased to 135% of its previous amount.
"increased to" denotes that we will multiply our original income by the percentage given.
Therefore our income would be = $X * 1.35 = $1.35
X
In the second case:
2) We received a raise and our income increased by 135%.
"increased by" denotes that we have to add the given percentage of our income to our original income.
Therefore our income would be $X + $X*1.35= $2.35X
