I guess the answer is A. Only statement 1 is sufficient but not 2.

My approach is "AD/BCE"
In order to know the amount of water to be added we need to know the amount of acid present & the initial amount of solution.
Statement -1:: 50 grm solution & 35% acid = .35X50 = 17.5 gms acid. New solution will have 17.5 gms acid, which will make 10% of the total amount of the solution => total amount of solution = 175 gms => water to be added = 175 - 50 = 75 gms.
We can cancel 2nd part of AD/BCE i.e we are left with options A & D.
Statement 2-:: no new information is given. 35% acid solution => acid 35 gms & water 65 gms. Ratio 35/65 = 7:13. Tgis is not sufficient. Therefore option D is also wrong.
We are left with A. Which I think is the correct option.

please let me know what you think....

For DS problem I always group the answer choices and work my way through by eliminating them till I get to the correct one.
I keep options A&D together and options BCE together and separate them by a "/" . it looks something like "AD / BCE". Then I go to the statements.
Now consider: (case I)
If statement 1 is sufficient
Then there are only two possibilities either only statement 1 is sufficient and 2 is not which gives you answer "A", or statement 2 is also sufficient that means both of them are sufficient which gives you answer choice "D". So keep them & cancel the other three option BCE. you are left with AD / [strike]BCE[/strike], you can straight way eliminate BCE. Consider the answer options, "B" = only 2, is wrong since 1 is already giving you the answer, "C" = combined, wrong, since 1 is already giving you the answer, "E" = not sufficient, since 1 is already giving you the answer.

Now that you are left with only 2 options A & D and the problem becomes bit simpler. You need only to check whether 2 is also sufficient. If 2 is then cancel out A & go for "D". Otherwise stick to A.
(case II)
If statement 1 is not sufficient
Then you can cancel out A&D and write [strike]AD[/strike] / BCE. now check for statement 2 and see whether it gives you an answer. If it does then B is the answer, if it does not then you have to check by combining. If that also fails then the answer is E.
I am just applying POE (process of elimination ) at the beginning to simplify my task and work with fewer answer choices.
Hope the explanation is clear. Its a bit lengthy but I could not manage to keep it more simple.