Solution:

They can say this line only on Thursday.

Explanation:
Let us analyze the statement. If the person who is speaking this line is speaking truth, then the person will have to speak a lie on the next day. But if the person is lying, the next day, that person must speak truth on the next day.

If you notice here, the behavior is changing on the next day no matter what the person speaks. If we create a response table for both Jack and Rose, it will look like this:

Jack Rose
Monday Truth Truth
Tuesday Truth Lie
Wednesday Truth Lie
Thursday Truth Lie
Friday Lie Truth
Saturday Lie Truth
Sunday Lie Truth

Now as you can clearly see, Jack can say this statement on Thursdays and Sundays while Rose can say this statement on Mondays and Thursdays.

Since they are saying on the same day, the required day is Thursday.

Solution:

There is only one way to do it. The old man must ask one of his son to divide the land in two parts and then ask the other one to pick up any land he want from the two. In this way, the first son will try to be fair and the second one won't mind as he will get to choose one first.

Solution:

Yes it is absolutely possible. Actually Tuesday is the name of his car.

Solution:

The barman noticed that the man was hiccupping badly while he ordered for his drink. Thus to give him a shock, he pulled out a gun and aimed for his head. This shock ultimately cured his hiccups.

Solution:

Did you concentrate on the point that it was a ping pong ball? Also that you have a water bottle with you. We never mentioned that it was empty. So what you will do is simply empty it in the narrow pipe and the ball will come up floating on the water. All the other things that were mentioned served just as distractions and if you were not able to find a way, they all worked quite well.

Solution:

Nothing is the name of a boat that has been lying docked up to one corner of the island. You found it first and then the torn pieces of paper reviled a map that can be used to navigate while driving that ship. Thus using them, you will be able to make an escape.

Solution:

I have just two tee shirts neither of which are green, blue or orange in color.

Solution:

That person in the picture is the son of the man holding the picture.

Solution:

It is perfectly feasible. The forty elephants had forty foreheads.

Solution:

The worth of that coin is zero. This is because the B.C. and A.D. dating system was not empowered till the year 525. So the coin is probably fake.