Solution:

You should reject the bet. When you give him $100, he won't be able to convert it into $500 dollar and will lose the bet. Thus, he'll give you $50. But your $100 will be with him and therefore, you are going to lose your money anyhow

Solution:

The mules is moving in circular path and hence outside legs travels more distance than inner legs.

Solution:

She is near the trunk of the tree as shown below.

Solution:

Birbal drew another line that was larger than the pre-drawn line. Now the pre drawn line was smaller.

Solution:

Six.

There are only five colors, so six socks guarantee that two will be the same color.

Solution:

   9567
+ 1085
======
 10652

Solution:

Bond was suspicious of the women as one never knocks its own door at the hotel.

Solution:

3/7

Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.

Solution:

The attached picture gives away the solution. If you can find another solution, do send us yours.

Solution:

1. Fill 5 liters jar ( 5l-jar:5, 3l-jar:0)
2. Transfer to 3 liters pail (5l-jar:2, 3l-jar:3)
3. Empty 3 liters jar ( 5l-jar:2, 3l-jar:0)
4. Transfer 2q from 5 pail to 3 pail (5l-jar:0, 3l-jar:2)
5. Fill 5 liters pail(5l-jar:5, 3l-jar:2)
6. Transfer 1q from 5 pail to 3 pail(5l-jar:4, 3l-jar:3)

Solution:

Let us denote the number of boys as 'p' and the number of girls as 'q'.

The first statement says that each boy has equal numbers of brothers and sisters
(p - 1) = q
=> p - q = 1 ------- (a)

The second statement says that every girl has twice as many brothers as that of sisters
2 (q - 1) = p
=> 2q - p = 2 ------- (b)

By solving (a) and (b)
We get q as 3 and p as 4.

Therefore, there are 4 boys and 3 girls in the family.