If the sum of the number 842 and two other numbers obtained by arranging the digits in cyclic order is divided by :

(i) 111

(ii) 14

(iii) 37

(i) According to the property 3, when abc + bca + cab is divided by 111, the quotient = a + b + c.

Here the number is 842 and when it is arranged in cyclic order it becomes 428 and 284.

When 842 + 428 + 284 is divided by 111, the quotient = 8 + 4 + 2 = 14.

(ii) According to the property 3, when abc + bca + cab is divided by a + b + c, the quotient = 111 .

Here the number is 842 and when it arrange in cyclic order it becomes 428 and 284.

When 842 + 428 + 284 is divided by 8 + 4 + 2 (14), the quotient = 111.

(iii) Here the number is 842 and when it arrange in cyclic order it becomes 428 and 284.

$\dfrac{842 + 428 + 284}{37}\\[1em] = \dfrac{1554}{37}\\[1em] = 42$

When 842 + 428 + 284 is divided by 37, the quotient = 42.