For a 3-digit number abc, what will be the quotient if abc – cba is divided by 11 ?

As we know abc = 100 x a + 10 x b + c.

Similarly, cba = 100 x c + 10 x b + a.

Hence,

$\dfrac{abc - cba}{11}\\[1em] = \dfrac{(100 \times a + 10 \times b + c) - (100 \times c + 10 \times b + a)}{11}\\[1em] = \dfrac{100a + 10b + c - 100c - 10b - a}{11}\\[1em] = \dfrac{(100a - a )+ (10b - 10b) + (c - 100c)}{11}\\[1em] = \dfrac{(99a ) + (- 99c)}{11}\\[1em] = \dfrac{99 (a - c)}{11}\\[1em] = 9(a - c)$

Hence, if abc – cba is divided by 11 then the quotient is 9(a-c).