If sum of the number 985 and two other numbers obtaind by arranging the digits of 985 in cyclic order is divided by 111 , 22 and 37 respectively.

Find the quotient in each case.

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Solution

The given number is 985

The other two numbers by arranging its digits in cyclic order, will be 859,598 of the form

$¯ ¯¯¯¯¯¯ ¯ a b c, ¯ ¯¯¯¯¯¯ ¯ b c a, ¯ ¯¯¯¯¯¯ ¯ c a b$

Therefore,

If 985+859+598 is divided by 111,then quotient will be a+b+c=9+8+5=22

If this sum is divided by 22, then the quotient =111

and if it is divided by 37, then quotient =3(a+b+c)=3(22)=66

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If sum of the number 985 and two other numbers obtaind by arranging the digits of 985 in cyclic order is divided by 111 , 22 and 37 respectively. Find the quotient in each case.

If sum of the number 985 and two other numbers obtaind by arranging the digits of 985 in cyclic order is divided by 111 , 22 and 37 respectively.

Find the quotient in each case.