Find the value of A , B and C in 1) AB x BA=BCB
​ 2)AB + BA=(B+1)CB

Answer :

1 :
12 $\times$ 21  = 252

Here we get our equation in form of given equation AB $\times$ BA  = BCB , After comparing 
So,
A  =  1  , B  =  2 and C  = 5

2 ) We have  :  AB $\times$ BA  = ( B  +  1 )CB

Here we have two digit number multiplied by same two digit with different place value , that gives three digit number .

So, we check

20 $\times$02  =  40   ( That only gives us 2 digit number )

19 $\times$ 91  = 1729 ( That gives four digit number )

18 $\times$ 81  = 1458 ( That gives four digit number )

17 $\times$ 71  = 1207 ( That gives four digit number )

16 $\times$ 61  = 976 ( That gives three digit number ) , But we can't write 9 = B + 1  where B  = 6

15 $\times$ 51  = 765 ( That gives three digit number ) , But we can't write 7 = B + 1  where B  = 5

14 $\times$ 41  = 574 ( That gives three digit number ) , Here we can  write 5 = B + 1  where B  =4

SO, we can say

A  =  1  ,  B  = 4  and C  = 7                               (  Ans )

And
13 $\times$ 31  = 403 ( That gives three digit number ) , Here we can  write 4 = B + 1  where B  = 3

SO, we can say

A  =  1  ,  B  = 3  and C  = 0                               (  Ans )