Solution:

A = B = K =6
C =7
D = H = 1,
E=0 ,
F = I = G = 4,
J=3,
L=5

Now we can rewrite the equations as :
66 = 76 - 10
44 = 60 - 14
16 = 64 - 46
37 = 67 - 30
35 = 53 - 16
10 = 74 - 64

Solution:

One of the cop will move clockwise while the other will move anti-clockwise every day. In such a manner, they will catch the thief in minimum seven days.

Solution:

I + IX = X

The equation read from the other side becomes X = XI + I which is false.

Solution:

41312432

Solution:

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

Solution:

The two numbers are 4 and 13 whose product is 52 and sum is 17.

Solution:

73

Explanation:
It's a very famous puzzle known as "Josephus Problem Puzzle". It can be solved in various ways but the trick to solve this problem is illustrated below.

Binay number of 100 is: 1100100
complement pf 100 is 0011011, whose decimal equivalent is 27.
The desired answer will be 100 - 27 = 73

Solution:

Either your read from start or from ends, it will be same

Solution:

He simply suggested that one of the brothers will be allowed to divide the land but he must take into consideration that it will be the other one who will have a choice of selecting his land between the two halves first.

Thus both will be happy in such manner.

Solution:

19

Explanation:
The children can purchase 19 chocolates in return.

Out of 77 wrappers, 75 will be used to buy 15 chocolates and two will be left spare.
The 15 chocolates will create 15 empty wrappers that can be exchanged to get three chocolates.
Three chocolates will return three wrappers which will help them buy another chocolate.
Now the wrapper from this chocolate and the two spare that were left earlier will get them another chocolate.
15 + 3 + 1 = 19

Solution:

2003.

Explanation:
Its a series of prime numbes.