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Question Number 217535 by ArshadS last updated on 15/Mar/25

$$\mathrm{A}\mathrm{two}-\mathrm{digit}\mathrm{number}\mathrm{is}\mathrm{such}\mathrm{that}$$$$\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{its}\mathrm{digits}\mathrm{is}10.\mathrm{When}$$$$\mathrm{the}\mathrm{digits}\mathrm{are}\mathrm{reversed},\mathrm{the}\mathrm{new}\mathrm{number}$$$$\mathrm{is}28\mathrm{less}\mathrm{than}\mathrm{twice}\mathrm{the}\mathrm{original}\mathrm{number}.$$$$\mathrm{Find}\mathrm{the}\mathrm{original}\mathrm{number}.$$

Answered by aleks041103 last updated on 15/Mar/25

$$letthenumberbe\stackrel{\mathrm{\_}\mathrm{\_}}{ab}=10a+b$$$$weknow:$$$$a+b=10\Rightarrow b=10-a$$$$\stackrel{\mathrm{\_}\mathrm{\_}}{ba}=2\stackrel{\mathrm{\_}\mathrm{\_}}{ab}-28$$$$\Rightarrow 10b+a=20a+2b-28\Rightarrow 19a-8b=28$$$$\Rightarrow 19a-8(10-a)=27a-80=28$$$$\Rightarrow 27a=108\Rightarrow a=4\Rightarrow b=6$$$$$$$$Ans.46$$$$check:$$$$4+6=10✓$$$$2\times 46-28=92-28=64✓$$

Commented by ArshadS last updated on 16/Mar/25

$$\mathbf{T}\mathrm{hanks}\mathbf{s}\mathrm{ir}!$$

Answered by Rasheed.Sindhi last updated on 16/Mar/25

$$Leta\mathrm{\&}10-aaredigits$$$$\bullet Originalnumber=10a+(10-a)$$$$=9a+10$$$$\bullet Reversednumber=10(10-a)+a$$$$=100-9a$$$$\bullet 100-9a=2(9a+10)-28$$$$100-9a=18a+20-28$$$$27a=108\Rightarrow a=4$$$$Originalnumber=9\left(4\right)+10=46$$$$\mathcal{V}erification:$$$$Reversednumber=100-9\left(4\right)=64$$

Commented by ArshadS last updated on 19/Mar/25

$$\mathrm{Thanks}\mathrm{sir}!$$

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