Difference between a four digit number and its reverse is always divisible by

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Solution

The correct option is A
9

Let 4 digits number be abcd
abcd can also be written in the form 1000a +100b + 10c +d
Reverse of abcd is dcba which can be written as 1000d +100c + 10b +a
So, difference between them is(1000a +100b + 10c +d) - (1000d +100c + 10b+a)
= (999a + 90b - 90c - 999d) = 9(111a +10b -10c -111d)
So, difference is always divisible by 9

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