Solution:

2nd Feb

Explanation:
a.b X a/b = 1
2.5 x 2/5
= 5/5
= 1

Solution:

7 Trips

Explanation:
Send 2+5+9 = 16
Bring back 9
Send 3+4+9 = 16
Bring back 9
Send 1+7+8 = 16
Bring back 1
Send 1+6+9 = 16

Solution:

The cowboy can fit the horses as shown below.

[T] [E] [N] [H] [O] [R] [S] [E] [S]

Solution:

Pour 3 lumps on cup-1 and cup-3 and 4lumps on cup4 and place them as shown in the picture.

Explanation:
Now,
Cup-1 got three sugar lumps
Cup-3 got three sugar lumps
Cup-2 got three seven lumps (3 of cup-1 and 4 of its own)

Solution:

As the balloon lost altitude, all of the thieves took off their clothes in order to decrease the overall weight. but when balloon continues to lose the attitude they decide one of them need to jump to the desert to decrease the weight.
The man who must jump is decided by the famous death game where one who picks the shortest toothpick must die.
Frank Catton pick the half toothpick and was already naked and hence the hence explain his state in the desert.

Solution:

The node can be connected as shown.

Solution:

A

Explanation:
Pi = 3.141592653.....
All images are related by pi value i.e "The number of straight lines on each shape corresponds to the digits of pi."

Solution:

Terry was in the lift.

Solution:

Treasure Map Is Hidden Inside The Hanging Room Floor.

Explanation.
Just reverse the text "roolF mooR gnignaH ehT edisnI neddiH sI paM erusaerT".

Solution:

TIF56

Explanation:
The password is formed as:
T (5th letter of Shruti)
I (5th letter of Arshika)
F(1st letter of Friday)
5(5th day of week)
6(Length of Friday)

Similarly, we will pick the 1st letter for Monday and 3rd letter for Wednesday.