From a four digit number, a number formed by reversing the digits is subtracted. The new number is always divisible by

Correct option is D

Given:

From a four-digit number, the number formed by reversing its digits is subtracted.

Find the number by which the result is always divisible.

Solution:

If the four-digit number is abcd, then

Original number = 1000a + 100b + 10c + d

Reversed number = 1000d + 100c + 10b + a

Subtracting,

(1000a + 100b + 10c + d) - (1000d + 100c + 10b + a)

= 999(a-d) + 90(b-c)

= 9[111(a-d) + 10(b-c)]

So, the result is always divisible by 9