Solution:

38

Explanation:
The total number of triangles are 8.

Let us divide the triangles in three categories: small, medium and large.

If we start with the small triangles, you can count a total of 24 triangles. 12 triangles (3 + 4 + 3 + 2) are upward facing and 12 are downward facing.

Next, we count the medium sized triangles. You can find a total of 12 triangles. 6 triangles (3 + 2 + 1) are facing upwards and 6 are facing downwards.

Lastly, if you calculate the large triangles, they are only two. One is upward facing and one is facing downward.

24 + 12 + 2 = 38.

Solution:

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

Solution:

Ganpat had a black suit and a brown suit.
Harish had a brown suit and a pink suit.
Manoj had a white suit and a black suit.
Tarun had a pink suit and a white suit.

Solution:

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

Solution:

16

Explanation:
9 [1x1] squares
5 [2x2] squares
1 [4x4] square
1 [4x4] square

9 + 5 + 1 + 1 = 16 squares.

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:

Treasure Map Is Hidden Inside The Hanging Room Floor.

Explanation.
Just reverse the text "roolF mooR gnignaH ehT edisnI neddiH sI paM erusaerT".

Solution:

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

Solution:

36 meters.

100/v1 = 80/v2
100/v2 = 80/v3

20+(20/v2)*v3=20+16 = 36

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

Six.

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