Write the quotient when the difference between 694 and number obtained on interchanging its ones and hundreds digits is divided by :

(i) 33

(ii) 99

(iii) 2

Lets take the 3-digit number as abc

∴ Number obtained on interchanging its ones and hundreds digits will be cba

abc - cba

= (100a + 10b + c) - (100c + 10b + a)

= 100a + 10b + c - 100c - 10b - a

= (100a - a )+ (10b - 10b) + (c - 100c)

= (99a ) + (- 99c)

= 99 (a - c)

= 99(a - c)

Here a = 6, b = 9 and c = 4

(i) On dividing by 33:

$\dfrac{99(a - c)}{33} \\[1em] = 3(a - c)$

Substituting values of a and c we get,

3(6 - 4) = 3 x 2 = 6

∴ When the difference between 694 and number obtained on interchanging its ones and hundreds digits is divided by 33, its quotient will be 6.

(ii) On dividing by 99:

$\dfrac{99(a - c)}{99} \\[1em] = (a - c)$

Substituting values of a and c we get,

6 - 4 = 2

∴ When the difference between 694 and number obtained on interchanging its ones and hundreds digits is divided by 99, its quotient will be 2.

(iii) On dividing by 2:

$\dfrac{99(a - c)}{2}$

Substituting values of a and c we get,

$\dfrac{99(6 - 4)}{2} \\[1em] = \dfrac{99 \times 2}{2} \\[1em] = 99$

∴ When the difference between 694 and number obtained on interchanging its ones and hundreds digits is divided by 2, its quotient will be 99.