Let xy be the two-digit number. The two-digit number xy can be written as =10x+y The interchanged two-digit number =yx=10y+x According to the question, ⇒10x+y−(10y+x)=45 ⇒10x+y−10y−x=45 ⇒9x−9y=45 ⇒x−y=5 Now, The product of the digits of the original number =x×y=14 Since (a+b)2−(a−b)2=4ab Therefore, ⇒(x+y)2−(x−y)2=4xy ⇒(x+y)2−(5)2=4×14 ⇒(x+y)2−25=56 ⇒(x+y)2=81 ⇒(x+y)=9 Therefore, The sum of the digit of the original number =9 ∴ The required answer is 9 .