If ABB ×999=ABC123(where A, B, C are digits) find the values of A, B, C

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Solution

In table of 999, last 3 digit decreased by by one each time .
9991=999
9992=1998
9993=2997
so after (1000 -123 =) 877 times last 3 digit will be 123 .
here we can see that it is in abb pattern .
So value of abc can be 877 .
Now putting the value of abb = 877 we get abb999 = 876123 .
which is satisfying the RHS .
So value of a,b,c will be 8,7,6 respectevely

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