Solution:

19

Explanation:
The Cost of 1st Wizard is: 50 i.e Total coins spend: 50
The Cost of 2nd Wizard is: 100 i.e Total coins spend: 150
The Cost of 3rd Wizard is: 150 i.e Total coins spend: 300
The Cost of 4th Wizard is: 200 i.e Total coins spend: 500
The Cost of 5th Wizard is: 250 i.e Total coins spend: 750
The Cost of 6th Wizard is: 300 i.e Total coins spend: 1050
The Cost of 7th Wizard is: 350 i.e Total coins spend: 1400
The Cost of 8th Wizard is: 400 i.e Total coins spend: 1800
The Cost of 9th Wizard is: 450 i.e Total coins spend: 2250
The Cost of 10th Wizard is: 500 i.e Total coins spend: 2750
The Cost of 11th Wizard is: 550 i.e Total coins spend: 3300
The Cost of 12th Wizard is: 600 i.e Total coins spend: 3900
The Cost of 13th Wizard is: 650 i.e Total coins spend: 4550
The Cost of 14th Wizard is: 700 i.e Total coins spend: 5250
The Cost of 15th Wizard is: 750 i.e Total coins spend: 6000
The Cost of 16th Wizard is: 800 i.e Total coins spend: 6800
The Cost of 17th Wizard is: 850 i.e Total coins spend: 7650
The Cost of 18th Wizard is: 900 i.e Total coins spend: 8550
The Cost of 19th Wizard is: 950 i.e Total coins spend: 9500
The cost of 20th Wizard is: 1000 i.e Total coins spend: 10500 .... more than 10,000.

Solution:

142857

Explanation:
142857 * 1 = 142857
142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
142857 * 6 = 857142

Note: Such numbers are called cyclic numbers.

Solution:

11

Explanation:
We are looking at the numbers in the form of 5k +1 or 5k + 3
i.e The number ends in 1 or 3
If we jot down all such numbers, there are 16 in total:
1, 3, 11, 13, 21, 23, 31, 33, 41, 43, 51, 53, 61, 63, 71 and 73

Now, let us remove the ones that are not prime and we have the answer as:
3, 11, 13, 23, 31, 41, 43, 53, 61, 71 and 73

Solution:

Horse = 10
Cowboy-Boot = 1
HorseShoe= 2
The Last equation = 21

Detailed Explanation :
Equation1:
3Horse = 30
=> Horse = 10 .....(1)

Equation2:
1Horse + 2HorseShoe + 2HorseShoe = 18
10 + 4HorseShoe =18
HorseShoe = 2 .....(3)

Equation3:
2HorseShoe - 2Cowboy-Boot = 2
4 - 2Cowboy-Boot = 2
=> Cowboy-Boot = 1 ... (2)

Equation4:
Cowboy-Boot+Horse*HorseShoe = 1+10*2
=>21

Solution:

10

Explanation:
Equation 1 + 9 + 11 = 1 can be derived from
One (o) + nine (n) + eleven (e) = one => 1

Similarly for equation,
12 + 11 + 9
Twelve (t) + eleven (e) + nine (n) => ten (10)

Solution:

The solution is provided in the image below.

Solution:

9 - 8 + 76 - 5 + 4 + 3 + 21 = 100


Other ways of making number 100 (withiout using number 32)
98 + 7 + 6 - 5 - 4 - 3 + 2 - 1 = 100
98 - 7 - 6 - 5 - 4 + 3 + 21 = 100
9 - 8 + 76 - 5 + 4 + 3 + 21 = 100
98 - 7 + 6 + 5 + 4 - 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 + 3 - 2 - 1 = 100
98 + 7 - 6 + 5 - 4 - 3 + 2 + 1 = 100
98 - 7 + 6 + 5 - 4 + 3 - 2 + 1 = 100
98 - 7 + 6 - 5 + 4 + 3 + 2 - 1 = 100
98 + 7 - 6 - 5 + 4 + 3 - 2 + 1 = 100
98 - 7 - 6 + 5 + 4 + 3 + 2 + 1 = 100
9 + 8 + 76 + 5 + 4 - 3 + 2 - 1 = 100
9 + 8 + 76 + 5 - 4 + 3 + 2 + 1 = 100

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:

930

Explanation:
New number = Last number * multiplication factor (increased by 0.5 every time) + sum factor (increased by 5 every time)
10
10 * 0.5 + 5 => 10
10 * 1.0 + 10 => 20
20 * 1.5 + 15 => 45
45 * 2.0 + 20 => 110
110 * 2.5 + 25 => 300
300 * 3.0 + 30 => 930 , desired answer

Solution:

30%

Explanation:
√9%
=> √9/√100
=> 3/10
=> 30/100
=> 30%