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P Pankaj Sanodiya
The addition of A and B is giving a number whose ones digit is 9. The sum can only be 9 not 10 as a sum of two single digits cannot exceed 18. hence there will not be any carry for the next step  2 + A = 0  implies A = 8  2 + 8 = 10 and 1 is the carry for next step. 1 + 1 + 6 = A = 8  it satisfies hence A = 8 and B = 1 is the correct answer.

P Pankaj Sanodiya
The additiion of B and 1 is 8  is giving a number whose ones digit is 8. this means digit B is 7 .  B + 1 = 8 and no carry for next step. next step : Now, A + B = 1 => A + 7 which implies A = 4  A  + B = 11 and 1 is carry for next step  1 + 2 + A  = B 1 + 2 + 4 = 7  Hence A = 4 and B = 7 is correct answer.

P Pankaj Sanodiya
The addition of 1 and B gives a number whose ones digit is 0. this is possible when digit B = 9 .  1 + B  = 10  and 1 is the Carry for the next step  Now, A + 1 + 1 = B => 9 Implies  A = 7. Hence A = 7 and B = 9 is Correct answer

P Pankaj Sanodiya
The product of 6 & B gives a number whose unit digit is B again. possible value of B = 0. 2 , 4, 6 or 8  If B = o then our product will be zero. hence this value of B is not possible. If B = 2, then B x 6 = 12 . Carry for next step = 1. 6A + 1 = BB = 22 implies A = 21/6 = not any integer value hence this case is also not possible. If B = 6  then B *6 = 36 and 3 will be carry for next step. 6A +...

P Pankaj Sanodiya
Here , multiplication of B and 5 gives a number whose ones digit is B. this is possible when B = 0 or 5 let B = 5  B * 5 = 5 * 5 = 25 Carry = 2 5*A + 2 = CA  , This os possible only when A = 2 or 7 when A = 2 , 5*2 + 2 = 12 which implies C = 1 when A = 7  5*7 + 2 = 37 which implies C = 3   now  B = 0  B*5 = 0*5 = 0  Carry = 0 so  5 * A = CA which is possible when A = 0 or 5 Howerver A cannot...

P Pankaj Sanodiya
Here multiplication of 3 and B gives  a number whose unit place digit is B . Possible value of B = 0 and 5 let B = 5  3 * A  + 1 = CA this is not possible for any value of A.  Hence B = 0 now  A * 3 = CA ( a number whose unit place digit is A itself when multiplied by 3) hence  possible value of A = 5 and 0  since AB is a two digit number A can not equal to 0. hence A = 5  A * 3 + 1 = CA 5 * 3...

P Pankaj Sanodiya
There can be two cases 1. when the addition of unit place digit doesn't  produce Carry A + 3 = 6 A = 3 However, to get 3 in unit place of our answer our B has to be 6 and that would produce carry hence this case is not possible. 2. when the addition of unit place digit produces Carry A + 3 +1 = 6 A = 2 for getting 2 in unit place of answer we need the sum of unit digit of numbers = 12 B + 7 =...

P Pankaj Sanodiya
Here first clue : we have A = a number which when multiplied by itself gives the same number in the unit digit.  possible numbers = 1 and 6  Second Clue: number when multiplied with 1 and added with the reminder of previous multiplication( A*A) = 9  both first and second clue implies that A = 6.