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

Let the digits of the number be a, b and c taken in order.
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.

  • 15
a+b+c
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