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If the number abcd is divisible by 11 then [ (b + d) - (a + c) ] also must be divisible by 11.
let the number be 1089
here a = 1, b = 0, c = 8 and d = 9
1089 = 1000*1 + 100*0 + 10*8 + 9
= (1001*1 + 99*0 + 11*8) + [(0 + 9) - (1 + 8)]
= 11(91*1 + 9*0 + 8) + [ 9 - 9 ]
here [ (b + d) - (a + c) ] = [9 - 9 ] = 0 which is divisible by 11.
hence If the number abcd is divisible by 11 then [ (b + d) - (a + c) ] also must be divisible by 11.