A-two-digit-number-is-such-that-the-sum-of-its-digits-is-10-When-the-digits-are-reversed-the-new-number-is-28-less-than-twice-the-original-number-Find-the-original-number-

FacebookTweetPin

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

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

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

FacebookTweetPin