Answer to Game No 1:   Calculate the addition of 1 to 10 numbers?

Add the first number and last number, Then multiply it with the half of the last number. For example:

addition of first and last number:  1 + 10 = 11
multiply by half of the last number:  (1 + 10) x 10/2
so 11 x 5 = 55

Answer to Game No 2:  Laddoo for Guests

These questions are solved from the end.

The 5th guest ate 16 Laddoo, it means the 4th guest left 8 Laddoo.
The 4th guest also ate 16 Laddoo, so it means that he was offered 16 + 8 = 24 Laddoo. He ate 16 and left 8.
Since the 4th guest received 24 Laddoo, it means the 3rd guest left 12 Laddoo. He was offered 12 + 16 = 28 Laddoo.
Since the 3rd guest received 28 Laddoo, it means the 2nd guest left 14 Laddo. So he ate 16 and left 12.
Since the 2nd guest left 14 Laddo, and we know that he ate 16 Laddoo, he was offered 30 Laddoo. It means the 1st guest left 15 Laddoo.
Now the 1st guest also ate 16 Laddoo, so he was offered 31 Laddoo. He ate 16 and left 15 Laddoo.

1st guest was offered 31 Laddoo, he ate 16, left 15
2nd guest was offered 15 + 15 = 30, he ate 16, left 14
3rd guest was offered 14 + 14 = 28, he ate 16, left 12
4th guest was offered 12 + 12 = 24, he ate 16, left 8
5th guest was served with 8 + 8 = 16, he ate all, and went to sleep.

Answer to Game No 3: Telling the Addition of 5 Lines of 5 Digits Each Without Adding Them

Tell your friends that you could tell them the addition of 5 lines of 5 digit numbers without adding them. The condition is that they could write first 3 lines but the last 2 lines you will write.

So ask your partner to write a number of 5 digits. Now you draw a horizontal line a bit below (leaving the space for other 4 lines) and write a number thus: Subtract 2 from that number (or from the last 2 digits) and write that number starting with 2.

Now ask him to write the other two lines of 5 digit numbers below the first one. Now it is your turn to write the last two lines. Write your first line thus, that the friend's 2nd line and your line add to 99999. In the same way you write your second line too making the addition of friend's 3rd line and yours as 99999. Now the addition of all these 5 lines will have the same addition as you wrote before. Example:

Ram's first number       34576
Ram's second number    65743
Ram's third number      45870
your second line           34256      (making 99999 adding second line
your third line              54129      (making 99999 adding third line
_________________________________
                                234574

In the same way you can add 7 lines, or 9 lines, or 11 lines. In 7 lines, subtract 3 and keep 3 before the addition. In 9 lines, subtract 4 and keep 4 before the addition. In 11 lines subtract 5, and keep 5 before the addition. Leaving the first line aside, your lines and your friend's line must be of equal number. And your lines must be the complementary lines to his making each line as 99999.

Answer to Game No 4

Law:  Whatever number of people are involved in the game, multiply that number with the same number, same number of times, such as:
                             3 x 3 x 3 x 3 = 81

Now whatever number of people are there, subtract 1 from that number, and subtract the resultant from the above number
                              81 - (3 - 1 =) 2 = 79   Chapaatiyaan were made

Now keep dividing it among the number of people:

79 x 1/3 = 26 for Ram, 1 remaining for dog, 52 were kept
52 x 1/3 = 17 for Shyam, 1 remaining for dog, 34 were kept
34 x 1/3 = 11 for Sunder, 1 remaining for dog, 22 were kept
22 x 1/3 = 7 for each three, 1 remaining for dog.

Raam ate total Chapaatiyaan  26 + 7 = 33
Shyaam ate total Chapaatiyaan 17 + 7 = 24
Sundar ate total Chapaatiyaan 11 + 7 = 18
Dog got 1 + 1 + 1 + 1 = 4 Chapaatiyaan

Answer to Game No 5: How to Arrange Horses?

There were 32 horses which were standing like this:

Now remained 28 horses, they were arranged like this:

Then they were 36 horses, they were arranged like this:

Now Ram could count 12 horses from every side every time. So he could not know when the horses were taken away and when the horses were returned.