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  • The sum of the digits of a two-digit number is 15. The number obtained by reversing the order of the digits of the given number exceeds the given number by 9. Find the number.

The sum of the digits of a two-digit number is 15. The number obtained by reversing the order of the digits of the given number exceeds the given number by 9. Find the number.

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\\\text{Let the tens, unit digit of number be x, y respectively} \\ \text{Here, } $xy=10x+y$ \\ $\Rightarrow x+y=15$ \\ \text{Second condition:} \\ $\Rightarrow 10 y+x=9+10 x+y$ \\ $\Rightarrow 9 x-9 y=-9$ \\ $\Rightarrow x-y=-1$ \\ \text{Add resultant equations} \\ $\Rightarrow 2 x=14$ \\ $\Rightarrow x=7$ \\ $\Rightarrow y=8$ \\ \text{two digit number} $=78$

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