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Question 28

The sum of the digit of a two number is 15. If the digits of the given number are reversed, the number is increased by the square of 3. The original number is


Correct Answer: 78

Solution

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With tens digit $$t$$ and units digit $$u$$, $$t+u=15$$, and reversing increases the number by $$9$$: $$(10u+t)-(10t+u)=9$$, giving $$u-t=1$$. Solving together gives $$u=8$$, $$t=7$$, so the original number is 78.

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