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Question Number 170305 by MathsFan last updated on 20/May/22

$$\mathbf{A}\mathbf{number}\mathbf{with}\mathbf{two}\mathbf{digits}\mathbf{is}\mathbf{equal}\mathbf{to}$$$$\mathbf{four}\mathbf{times}\mathbf{the}\mathbf{sum}\mathbf{of}\mathbf{its}\mathbf{digits}.\mathbf{The}$$$$\mathbf{number}\mathbf{formed}\mathbf{by}\mathbf{reversing}\mathbf{the}\mathbf{order}$$$$\mathbf{of}\mathbf{the}\mathbf{digit}\mathbf{is}27\mathbf{greater}\mathbf{than}\mathbf{the}\mathbf{given}$$$$\mathbf{number}.\mathbf{Find}\mathbf{the}\mathbf{number}$$

Answered by Rasheed.Sindhi last updated on 20/May/22

$$Letthe2-digitnumberisx$$$$anditsreversednumberis{x}^{\prime }$$$$\therefore sumofdigits=\frac{x+x^{\prime }}{11}$$$$\left(1\right):$$$$x=4\left(\frac{x+x^{\prime }}{11}\right)\Rightarrow 11x=4x+4x^{\prime }\Rightarrow x^{\prime }=\frac{7x}{4}$$$$\left(2\right):$$$$x^{\prime }=x+27$$$$\frac{7x}{4}=x+27$$$$7x=4x+108$$$$3x=108$$$$x=36$$

Commented by otchereabdullai@gmail.com last updated on 21/May/22

$$\mathrm{nice}!$$

Commented by peter frank last updated on 21/May/22

$$\mathrm{thank}\mathrm{you}$$

Answered by floor(10²Eta[1]) last updated on 20/May/22

$$10\mathrm{a}+\mathrm{b}=4(\mathrm{a}+\mathrm{b})$$$$\Rightarrow 6\mathrm{a}=3\mathrm{b}\Rightarrow 2\mathrm{a}=\mathrm{b}$$$$10\mathrm{b}+\mathrm{a}=27+10\mathrm{a}+\mathrm{b}\Rightarrow 9\mathrm{b}=9\mathrm{a}+27$$$$\Rightarrow \mathrm{b}=\mathrm{a}+3\Rightarrow 2\mathrm{a}=\mathrm{a}+3\Rightarrow \mathrm{a}=3\Rightarrow \mathrm{b}=6$$$$\mathrm{the}\mathrm{number}\mathrm{is}36$$

Commented by MathsFan last updated on 20/May/22

$$thankyousir$$

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