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Question

The digits of a two-digit number differ by $$3$$. If the digits are interchanged and the resulting number is added to the original number, we get $$143$$. What can be the original number?


Solution

Let the digits of the number be $$a$$ and $$b$$ such that the number is $$(10a+b)$$.

According to the question,
$$a-b=3$$ or $$b-a=3$$    ...... (1)
$$10a+b+10b+a=143$$
$$a+b=13$$        ...... (2)

Solving both the equations, we have
$$a=8$$ and $$b=5$$ or $$a=5$$ and $$b=8$$

Therefore, the required number is $$85$$ or $$58$$.

Mathematics

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