Solution:

He will hang clock number 315 at 7:30pm. The person has been hanging the clock number which corresponds with the angle between the hour hand and the minute hand of the clock at that time.

Solution:

The answer is simple. The trains will be at same distance from Point P when they meet speaking on approximation. However, the train A will be closer to the point P by its own length if we are not taking meeting of train as perfectly overlapping.

Solution:

When the boats meet for the first time, they have sailed a combined distance that is equal to one length of the lake. When they meet the second time, they have sailed 3 lengths. The elapsed time and the distance for each is three times.

When they meet for the second time, the boat M has sailed 500 x 3 = 1500 yards. Now, this is 300 yards longer than the length of the lake, it must be 1200 yards wide.

The ration between the speed of boat M and boat N is equal to the ratio of the distance that they have sailed before they meet the first time.

Solution:

29 rungs.
Since he is standing on the middle rung in the beginning,
Let the middle rung be x
He climbs 6 rungs first and then climbs down rungs and again climbs 18 rungs to reach the top.
Thus the position is now,
X+6-10+18 = x + 14.
This position is on the top rung.
Thus the ladder has 14 rungs above the middle rung and also it must be having 14 rungs down the middle point as well.
14+14+1 = 29.
Thus there are total 29 rungs in the ladder.

Solution:

10992

Explanation:
Each girl has seven bags with seven adult cats each.
Also, each adult cat has seven little cats.
Thus each girl has 49 adult cats and 343 little cats.

Hence, seven girls will have
343 adult cats and 2410 little cats.

If we calculate the number of legs now.
Girls = 7 * 2 = 14
Cats + Little cats = 2744 * 4 = 10976

Total legs = 10976 + 14 = 10990

Since I also walked in the room, there will be two more legs.
Now total legs = 10990 + 2 = 10992.

Solution:

5832/17496
This fraction will give the desired result i.e. 1/3.

Solution:

If we place a decimal between the numbers it will become 5.9 which is what we needed.

Solution:

When fifteen minutes have passed, the hour hand has already moved exactly one fourth of an hour. Thus the angle between the hour hand and minute hand will be of 7.5 degrees.

Solution:

I had 10 candies in the beginning.

Explanation:
Let us take and solve this problem in the reverse direction.

At the end, I was left with 1 candy. Let me take the extra one candy back from my younger son. Now since I gave him half of what I had, we must be having the same number of candies. I have 2, which means he also have 2. This implies that I was left with 4 candies after I gave some to the elder son.

Let me take back the extra candy from my elder son now. Now I have 5 candies. Since I gave him half of what I had, he must be having 5 candies as well. Thus, I had 10 candies in the beginning.

Solution:

The number is 37.

The missing guess can be either 24 or 50 and the missing difference is 8.