Let the unit's digit of the number be and ten's digit be x ⇒ Number = 10x+y Product of digits = xy=18 ---(i) According to question, ⇒ 10x+y+63=10y+x ⇒ 9y−9x=63 ⇒ y−x=
63
9
=7 ------(ii) Substituting value of y from equation (ii) in (i), we get : ⇒ x(7+x)=18 ⇒ x2+7x−18=0 ⇒ x2+9x−2x−18=0 ⇒ x(x+9)−2(x+9)=0 ⇒ x=2,−9 Since x is a digit and can't be negative, ⇒ x=2 Substituting it in equation (ii), ⇒ y=7+2=9 ∴ Number = 29