Let the two-digit number be 10x+y, where x and y are the digits at the ten's and one's place respectively. 10x+y=k(x+y)....(1) 10y+x=m(x+y)......(2) Adding (1) and (2), we have 11x+11y=(k+m)(x+y) ⇒k+m=11 ⇒m=11−k Trick :Consider two–digit numbers 12=4×(1+2)⇒k=4 Now, 21=m×(1+2)⇒m=7 Now, 7=11−4 ∴m=11−k