Question

A number consists of two digits. Sum of its digits is 15. If the place of digits is interchanged then the number so obtained is 9 less than the original number. Find the original number

Answer 1

Dear Student,

$$\begin{gathered} Letthenumberwithtwodigitsbe10x+y \\ sumofthedigits=15 \\ So,x+y=15....\left(1\right) \\ Numberformedbyinterchangingthedigits=10y+x \\ Now,\left(10x+y\right)-\left(10y+x\right)=9 \\ 9x-9y=9 \\ x-y=1....\left(2\right) \\ Addingequ.\left(1\right)and\left(2\right),weget \\ x+y+x-y=15+1 \\ 2x=16 \\ \mathit{x}\mathbf{=}\mathbf{8} \\ Similarly,y=15-8 \\ \mathit{S}\mathit{o}\mathbf{,}\mathbf{}\mathit{y}\mathbf{=}\mathbf{7} \\ \mathit{T}\mathit{h}\mathit{e}\mathbf{}\mathit{n}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{i}\mathit{s}\mathbf{}\mathbf{80}\mathbf{+}\mathbf{7}\mathbf{=}\mathbf{}\mathbf{87} \end{gathered}$$

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