Solution:

Let us try to find average here.
The average number of hands per person among the people with one hand is 1 obviously.

Now in the remaining slot, half people have 1 arm and half have 2 arms. Therefore, the average arm per person is 1 only.

Now, if we combine both the results, we can conclude that the number of arms per person in that locality is 1.

Since the number of people living there is 200 in number, the number of arms will be 200 as well.

Solution:

The probability is 5/36.

Event = {(1,5) , (2,4), (3,3), (4,2), (5,1)}
Therefore, P (getting sum = 6) = 5/36

Solution:

The total number of students is 500.

To follow how and why, please see the venn diagram.

Solution:

102

Explanation:
The total number of animals in the zoo is one hundred and two i.e. thirty-four animals of each kind.

Since we already know that the number of each animal is same, each single deer, spider and cricket will have a total of eighteen legs.

Now, 612/18 = 34.

Therefore, total number of animals:
34 * 3 = 102

Solution:

28 is the required number.

28 * 3 - 2 = 82.

Solution:

16

Explanation:
Let the number be p, then the square will be p^2
According to question:
2p = (p/4) + 7
=> 8p = p + 28
=> p = 4

p^2 = 4^2 = 16.

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:

Box A has five balls and Box B has seven balls.

Solution:

The number is 281.

Solution:

18

Explanation:
Number of days with snow in morning and clear afternoon = A
Number of days with clear morning and snow in afternoon = B
Number of days with no snowfall in morning or afternoon = C

Now, number of days with snowfall = A + B = 13
Number of days with clear mornings = B + C = 11
Number of days with clear afternoons = A + C = 12

Adding these three equations, we get

2 * (A + B + C) = 36
Or, A + B + C = 18

Therefore, they spent eighteen days in total at their vacation.