11×11 = 121 = 171 in base 8
read here on how to convert one number from 10 base to another base
by following that:
121/8 = 15 R 1
15/8 = 1 R 7

= 1*8^2 + 7*8^1 + 1*8^0 = 171

thus 15×15 = 225
225/8 = 28 R 1
28/8 = 3 R 4
= 3*8^2 + 4*8^1 + 1*8^0 = 341

OR you can try this online tool to convert the base

Answer courtsey: George Georgiev

its the sum of all digits in the number till you get single digit
so 1+2+4+6 => 13 => 4

lets assume the amount in the check was x dollars and y cents
though he received y dollars and x cents

after spending 5 cents, his money is twice the amount on the check, i.e. 100y+x -5 = 2(100x + y)
98y = 199x + 5

we need to find two numbers in the exact multiple series of 98 and 199 which differs by 5.
98’s multiple series: 98,196,294,392,490,588,686,784,882,980,1078,1176,1274,1372,1470,1568,1666,1764,1862,1960,2058,2156,2254,2352,2450,2548,2646,2744,2842,2940,3038,3136,3234,3332,3430,3528,3626,3724,3822,3920,4018,4116,4214,4312,4410,4508,4606,4704,4802,4900,4998,5096,5194,5292,5390,5488,5586,5684,5782,5880,5978,6076,6174

199’s multiple series: 199,398,597,796,995,1194,1393,1592,1791,1990,2189,2388,2587,2786,2985,3184,3383,3582,3781,3980,4179,4378,4577,47764975,5174,5373,5572,5771,5970,6169,6368,6567,6766,6965,7164,7363,7562,7761,7960,8159,8358,8557,8756,8955,9154,9353,9552,9751,9950

 

98*63 = 199*31 +5

thus the amount on the check was 31 dollar and 63 cents.

Left side is the number of letters in the spelling of right side number

As 10, i.e. TEN has 3 letters, answer would be 3.

3 = 5 (March)
5 = 3 (May)
7 = 4 (July)
8 = 6 (August)
10 = 7 (October)
11 = 8 (November)
12 = 8 (December)