Question 1045477
a number consists of two digit the difference of whose digit is 5 if 8 times the number equals to 3 times the  number obtained by reversing the digit find the number

solution

{{{x-y}}}={{{5}}}

let original number be {{{10y+x}}}
reverse      number    {{{10x+y}}}
{{{8(10y+x)}}}={{{3(10x+y)}}}
{{{80y+8x}}}={{{30x+3y}}}  we know {{{x=5+y}}}
{{{80y+8(5+y)}}}={{{30(5+y)+3(y)}}}
{{{80y+(40+8y)}}}={{{(150+30y)+3(y)}}}
{{{88y+(40)}}}={{{(150+33y)}}}
{{{88y-33y+(40)}}}={{{(150)}}}
{{{88y-33y}}}={{{(150-40)}}}
{{{55y}}}={{{(110)}}}
{{{y}}}={{{(110)/(55)}}}
{{{y}}}={{{2}}}

using {{{y}}}={{{2}}}

{{{x=5+y}}}
{{{x=5+2}}}
{{{x=7}}}
hence {{{x=7}}},{{{y=2}}}
the number is {{{10y+x}}}
 {{{10*2+7}}}
 {{{27}}}
the reversed number
 {{{10x+y}}}
 {{{10*7+2}}}
 {{{72}}}
check 
 x is {{{7 }}} and y is  {{{2}}}
their difference is  {{{7-2}}}
 {{{5}}} check


the number   {{{27}}}
the reversed number  {{{72}}}
 {{{8}}}* {{{27}}}= {{{3}}}*{{{72}}}
 {{{216}}}= {{{216}}}

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