Solution:

This problem might seem complex but it can be solved completely using simple logics. We know that the bike is twice as fast as walking and thus the time taken by to reach hotel is equal to the time taken on foot to travel half the way. Thus, biking the whole way will be faster than taking the train if the train's speed is not infinite (not possible).

Solution:

The Lady sitting in the chair has the detector attached to the back of her blouse.

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

If you ask the guard who always tells the truth, he would tell you the other guard would point you to the door of death. If you ask the guard who always lies, he would tell you the opposite door of the truth-telling guard and point you to the door of death. In either case, both guards will point to the door of death so you should choose the other one.

Solution:

Read the question carefully again. New Year do falls after Christmas but that happens if two different years. The question is put up against the year 2050 and thus there will be 51 weeks and 2 days in between them as New Year will appear on 1 January 2050 and Christmas will happen on 25 December 2050.

Solution:

   9567
+ 1085
======
 10652

Solution:

The man asked the king that he wanted to die of old age.

Solution:

If you see the picture, they formed a pentagonal shape and achieved the required.

Solution:

What is the correct time ?

Solution:

The bridge won't break.

When the car has travelled half of the bridge, that is 15km, the car must have used more than 300 grams of fuel. Therefore, the impact of bird's added weight will be zero literally.

Solution:

5 leopard and one sheep

since all animal are rational , once 1st leopard eats the sheep all the rest of leopard would know about this.