If we multiply a certain two digit number by the sum of its digit we get 405 if we multiply the number consisting of the same digits written in the reverse order by the sum of the digits wicked 486 find the number

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Let the digit in units' place be y and the digit in tens' place be x.Hence the number is 10x+yReverse of number=10y+xGiven,The number multiplied by sum of its digits=40510x+y(x+y)=40510x² + 10xy+xy+y² = 40510x² + 11xy+y² = 405y² = 405 - 10x² - 11xy1Also,Reverse of number multiplied by sum of its digits=486(10y+x)(x+y)=48610xy+ 10y² +x² +xy= 48611xy+x² + 10y² = 4862Substituting 1 in 2,11xy+x² + 10(405 - 10x² - 11xy) = 48611xy+x² + 4050 - 100x² - 110xy= 486-99x² - 99xy+ 4050 = 48699x² + 99xy= 4050 - 48699(x² +xy) = 3564x² +xy=356499x² +xy= 36x(x+y) = 36x+y=36x   3Substituting 3 in 1,(10x+y)36x = 405360x+36y= 405x36y= 405x- 360x36y= 45xxy=3645xy=45x:y::4:5Hence,the 2 digit number is 10x+y10(4)+540+545
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