Solution:

father:72, Son:27

Explanation:
The only single digit prime numbers are 2, 3, 5 and 7.
Let us use the possible combinations and check when the difference comes to be 45.
Son = 23, Father = 32, Difference = 7
Son = 25, Father = 52, Difference = 27
Son = 27, Father = 72, Difference = 45

This stand apt for the requirements. Thus the present age of the father is 72 years and that of son is 27 years.

Solution:

Colors:
Y B R G
G R B Y
B Y G R
R G Y B


Signs:
x + - /
- / x +
/ - + x
+ x / -

Solution:

Tilt the barrel until the fruit juice barely touches the lip of the barrel. If the bottom of the barrel is visible then it is less than half full.If the barrel bottom is still completely covered by the fruit juice, then it is more than half full.

Solution:

7 Races.

Solution:

The husband had booked two tickets for departure and only one for the return. The travel agent told this information to the police and they immediately came to know that he had planned the murder right from the beginning.

Solution:

prinka is 10, in a system that awards five for each vowel.

Solution:

12 steps:

Steps 11 Liter jug 6 Liter Jug
1. 11 -
2. 5 6
3. 5 0
4. 0 5
5. 11 5
6. 10 6
7. 10 0
8. 4 6
9. 4 0
10. 0 4
11. 11 4
12. 9 6 ==> i found 9 liter in 11liter jug(as required)

Solution:

199 - 99

Solution:

Solution is shown in image below

Solution:

I + IX = X

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

Solution:

Solution can be verified from the picture below.