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Question Number 41877 by Tawa1 last updated on 14/Aug/18

$$\mathrm{The}\mathrm{tens}\mathrm{digit}\mathrm{of}\mathrm{a}\mathrm{two}\mathrm{digit}\mathrm{number}\mathrm{is}3\mathrm{greater}\mathrm{than}\mathrm{the}\mathrm{units}\mathrm{digit}.$$$$\mathrm{When}\mathrm{the}\mathrm{digits}\mathrm{are}\mathrm{reversed},\mathrm{the}\mathrm{number}\mathrm{is}\mathrm{reduced}\mathrm{by}27.$$$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{number}?$$

Answered by MrW3 last updated on 14/Aug/18

$${let}^{\prime }ssaythenumberisab$$$$a=b+3$$$$10\times b+a=10\times a+b-27$$$$\Rightarrow 9b=9a-27$$$$\Rightarrow 9b=9(b+3)-27$$$$\Rightarrow 0=27-27$$$$thisistrueforeverypossibledigitb,$$$$i.e.b=1,2,3,4,5,6$$$$sotherequestednumberisoneof$$$$41,52,63,74,85,96$$

Commented by Tawa1 last updated on 14/Aug/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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