Question

Sum of the digits of a two digit number is 9.
The number obtained by interchanging the digits differ the original number by 27. What is the original number?

Answer 1

Dear student,


$$\begin{gathered} Let\text{'}x\text{'}bethedigitatten\text{'}splaceand\text{'}y\text{'}bethedigitatunitplacerespectively. \\ therefore,thenumberwillbe,10\left(T\right)+U=10x+y \\ Numberobtainedbyinterchangingthedigit=10y+x \\ Accordingtoquestion, \\ 10x+y-\left(10y+x\right)=27 \\ \Rightarrow 10x+y-10y-x=27 \\ \Rightarrow 9x-9y=27 \\ \Rightarrow 9(x-y)=27 \\ \Rightarrow x-y=\frac{27}{9}=3 \\ \Rightarrow x-y=3......\left(1\right) \\ alsoitisgiven,x+y=9.....\left(2\right) \\ solving\left(1\right)and\left(2\right) \\ weget,2x=12 \\ \Rightarrow x=\frac{12}{2}=6 \\ from\left(1\right) \\ 6-y=3 \\ \Rightarrow -y=3-6=-3 \\ \Rightarrow y=3 \\ Thus,theoriginalnumber10x+y=10\times 6+3=60+3=63 \end{gathered}$$

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