A-number-with-two-digits-is-equal-to-four-times-the-sum-of-its-digits-The-number-formed-by-reversing-the-order-of-the-digit-is-27-greater-than-the-given-number-Find-the-number-

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

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

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

Let the 2-digit number is x and its reversed number is x′ ∴ sum of digits=((x+x′)/(11)) (1): x=4(((x+x′)/(11)))⇒11x=4x+4x′⇒x′=((7x)/4) (2): x′=x+27 ((7x)/4)=x+27 7x=4x+108 3x=108 x=36

$${Let}\:{the}\:\mathrm{2}-{digit}\:{number}\:{is}\:{x}\: \\ $$$$\:\:\:\:{and}\:{its}\:{reversed}\:{number}\:{is}\:{x}' \\ $$$$\therefore\:{sum}\:{of}\:{digits}=\frac{{x}+{x}'}{\mathrm{11}} \\ $$$$\left(\mathrm{1}\right): \\ $$$${x}=\mathrm{4}\left(\frac{{x}+{x}'}{\mathrm{11}}\right)\Rightarrow\mathrm{11}{x}=\mathrm{4}{x}+\mathrm{4}{x}'\Rightarrow{x}'=\frac{\mathrm{7}{x}}{\mathrm{4}} \\ $$$$\left(\mathrm{2}\right): \\ $$$${x}'={x}+\mathrm{27} \\ $$$$\frac{\mathrm{7}{x}}{\mathrm{4}}={x}+\mathrm{27} \\ $$$$\mathrm{7}{x}=\mathrm{4}{x}+\mathrm{108} \\ $$$$\mathrm{3}{x}=\mathrm{108} \\ $$$${x}=\mathrm{36} \\ $$

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

$$\mathrm{nice}! \\ $$

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

10a+b=4(a+b) ⇒6a=3b⇒2a=b 10b+a=27+10a+b⇒9b=9a+27 ⇒b=a+3⇒2a=a+3⇒a=3⇒b=6 the number is 36

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

Commented by MathsFan last updated on 20/May/22

$${thank}\:{you}\:{sir} \\ $$

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