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

Dear student,
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
Hope this information will clear your doubts about the topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

 
Regards

​​

  • 1
What are you looking for?