Question Number 170305 by MathsFan last updated on 20/May/22 | ||
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$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{digits}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{equal}}\:\boldsymbol{\mathrm{to}} \\ $$$$\boldsymbol{\mathrm{four}}\:\boldsymbol{\mathrm{times}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{digits}}.\:\boldsymbol{\mathrm{The}} \\ $$$$\boldsymbol{\mathrm{number}}\:\boldsymbol{\mathrm{formed}}\:\boldsymbol{\mathrm{by}}\:\boldsymbol{\mathrm{reversing}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{order}} \\ $$$$\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{digit}}\:\boldsymbol{\mathrm{is}}\:\mathrm{27}\:\boldsymbol{\mathrm{greater}}\:\boldsymbol{\mathrm{than}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{given}} \\ $$$$\boldsymbol{\mathrm{number}}.\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{number}} \\ $$ | ||
Answered by Rasheed.Sindhi last updated on 20/May/22 | ||
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$${Let}\:{the}\:\mathrm{2}-{digit}\:{number}\:{is}\:{x}\: \\ $$$$\:\:\:\:{and}\:{its}\:{reversed}\:{number}\:{is}\:{x}' \\ $$$$\therefore\:{sum}\:{of}\:{digits}=\frac{{x}+{x}'}{\mathrm{11}} \\ $$$$\left(\mathrm{1}\right): \\ $$$${x}=\mathrm{4}\left(\frac{{x}+{x}'}{\mathrm{11}}\right)\Rightarrow\mathrm{11}{x}=\mathrm{4}{x}+\mathrm{4}{x}'\Rightarrow{x}'=\frac{\mathrm{7}{x}}{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right): \\ $$$${x}'={x}+\mathrm{27} \\ $$$$\frac{\mathrm{7}{x}}{\mathrm{4}}={x}+\mathrm{27} \\ $$$$\mathrm{7}{x}=\mathrm{4}{x}+\mathrm{108} \\ $$$$\mathrm{3}{x}=\mathrm{108} \\ $$$${x}=\mathrm{36} \\ $$ | ||
Commented by otchereabdullai@gmail.com last updated on 21/May/22 | ||
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$$\mathrm{nice}! \\ $$ | ||
Commented by peter frank last updated on 21/May/22 | ||
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$$\mathrm{thank}\:\mathrm{you} \\ $$ | ||
Answered by floor(10²Eta[1]) last updated on 20/May/22 | ||
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$$\mathrm{10a}+\mathrm{b}=\mathrm{4}\left(\mathrm{a}+\mathrm{b}\right) \\ $$$$\Rightarrow\mathrm{6a}=\mathrm{3b}\Rightarrow\mathrm{2a}=\mathrm{b} \\ $$$$\mathrm{10b}+\mathrm{a}=\mathrm{27}+\mathrm{10a}+\mathrm{b}\Rightarrow\mathrm{9b}=\mathrm{9a}+\mathrm{27} \\ $$$$\Rightarrow\mathrm{b}=\mathrm{a}+\mathrm{3}\Rightarrow\mathrm{2a}=\mathrm{a}+\mathrm{3}\Rightarrow\mathrm{a}=\mathrm{3}\Rightarrow\mathrm{b}=\mathrm{6} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{is}\:\mathrm{36} \\ $$ | ||
Commented by MathsFan last updated on 20/May/22 | ||
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$${thank}\:{you}\:{sir} \\ $$ | ||