Number obtained by interchanging the digits of a two digit number is l

1.	Number obtained by interchanging the digits of a two digit number is less than the original number by 54, and the sum of the digit if 8. What is original two digit number?1). 622). 173). 714). 35
Answer» Let the unit digit of number be X and tenth digit be y Then, Number = 10y + x Number OBTAINED by reversing its digits = 10x + y Number obtained by interchanging the digits of a two digit number is less than the original number by 54 ∴ (10y + x) – (10x + y) = 54 ⇒ 9y – 9x = 54 ⇒ y – x = 6----EQ (1) Sum of the digits of the number = 8 ∴ y + x = 8----eq (2) By adding eq (1) and eq (2), we get 2y = 14 ⇒ y = 7 By putting this VALUE of y in eq(2), we get 7 + x = 8 ⇒ x = 1 ∴ Original two digit number = (10 × 7) + 1 = 71

Number obtained by interchanging the digits of a two digit number is less than the original number by 54, and the sum of the digit if 8. What is original two digit number?1). 622). 173). 714). 35

Answer»

Let the unit digit of number be X and tenth digit be y

Then,

Number = 10y + x

Number OBTAINED by reversing its digits = 10x + y

Number obtained by interchanging the digits of a two digit number is less than the original number by 54

∴ (10y + x) – (10x + y) = 54

⇒ 9y – 9x = 54

⇒ y – x = 6----EQ (1)

Sum of the digits of the number = 8

∴ y + x = 8----eq (2)

By adding eq (1) and eq (2), we get

2y = 14

⇒ y = 7

By putting this VALUE of y in eq(2), we get

7 + x = 8

⇒ x = 1

∴ Original two digit number = (10 × 7) + 1 = 71