Let the two digit number be 10x+y. According to the question, 10x+y=3(x+y) ⇒ 10x+y−3x−3y=0 ⇒ 7x−2y=0 ...(i) According to question ⇒ (10x+y)+45=10y+x ⇒ 10x+y+45−10y−x=0 ⇒ 9x−9y+45=0 ⇒ x−y=−5 ...(ii) Now, solving equations (i) and (ii), we get x=2 and y=7 digit =10×2+7=27 ∴ sum of the squares of digits =(2)2+(7)2 =4+49=53