The difference between a two-digit number and the number obtained by interchange the two digits of the number is 27. If the sum of the two digits of the number is 13, what is their product ?

• A. 39
• B. 37
• C. 40
• D. 38

Answer: (C)

Let the number be 10x + y.∴ 10x + y - (10y + x) = 27or 9x - 9y = 27∴ x - y = 3 .......(I)x + y = 13 .......(II)From eqn (I) and (II)x = 8 and y = 5.So the number = 85Therefore, product = 8 x 5 = 40