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