There are 2 two-digit numbers such that one is obtained by swapping the digits of the other. On subtracting one number by another, the result obtained is divisible by ___ .

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Solution

The correct options are
A
3

D
9

Let tens and ones digit of a number be a and b respectively.
Then, the number will be 10a + b.
The number obtained by swapping the digits will be 10b + a.

Upon subtracting, we get
(10a + b) – (10b + a)
= 10a + b – 10b - a
= 9a – 9b
= 9(a – b)

The number obtained is a multiple of 9, therefore it is divisible as well as by 3.

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