Two digit number is divisible by 9. Number when multiplied by sum of its digit is equal to 486. Given digits are unequal, find the number.

since a two digit number can be written as 10x+y where x and y are required numbers 

sum of digits is x+y and it gets multiplied by number which is 10x+y 

so (x+y)(10x+y)=486 

now when a number is divisible by 9 , the sum of digits of the number is 9 
( 18 =>1+8=9, 27=> 2+7=9, 36=>3+6=9, 54=> 5+4=9 and so on..) 

so we have sum of digits as x+y=9 

using in above equation (9)(10x+y)=486 
=> 10x+y = 54 ( dividing both side by 9) 

now solve these two equations 
subtracting both we have (10x+y)-(x+y)=54-9 
9x = 45 
x= 5 
so y=9-x=9-5=4 

hence number is 5x10+4=54 

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