Question

The product of the digits of a positive two digit number is 54. 27 is to be added in this number, the new number can be obtained by interchanging the digits of the original number. ​

Answer 1

let the number be 10x+y

given :

1.(x)(y)=54. ---(1)

2.10x+y+27=10y+x

9x-9y+27=0

divide by nine

x-y = -3. -----(2)

squaring both sides

(x-y)2 = 9

add 4xy both sides

(x-y)2 +4xy =9+4xy

(x+y)2 = 9+4(54). (from equation 1)

(x+y)2 =225

x+y= 15. ---(3)

add equation 1 and 3

2x= 12

x=6

put the value of x in equation 1

y= 9

original number is = 10x+y

= 10(6)+9

=69