# Without actual calculation write the quotient when the sum of 3-digit number abc and the number obtained by changing the order of digits cyclically i.e. bca and cab is divided by 111

i.e 100a+10b+c (original number) .....(1)

1 cyclic rotation will give: 100b + 10c + a .....(2)

2nd cyclic rotation will give: 100c + 10a + b .....(3)

sum of (1), (2) and (3) will give: (100a + 10b + c)+( 100b + 10c + a)+(100c + 10a + b ) =111a+111b+111c

on dividing 111a+111b+111c with 111 we will get: a+b+c

Hence, quotient is a+b+c.

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