The sum of digits of a two digit number is 14 and the difference between the number obtained by interchanging the digits and the original two digit number is 36. Find the original number.

Option 1 : 59

**Given:**

Sum of digits of a two digit number = 14

Difference between number obtained by interchanging and original number = 36

**Concept used:**

If the digit at unit's place is y and at ten's place is x, then the two digit number = (10x + y)

**Calculation:**

Let the original number be (10x + y)

According to the question,

(10y + x) - (10x + y) = 36

⇒ (9y - 9x) = 36

⇒ (y - x) = 4 ----(1)

Also, (y + x) = 14 ----(2)

Adding equations (1) and (2), we get

2y = 18

⇒ y = 9

Substituting (y = 9) in equation (1), we get

x = 5

Required number = (10 × 5) + 9

⇒ 59

**∴ The Original number is 59.**

**Concept used:**

If the sum of the digits of a two digit number is M. The number formed by reversing the digits is N more than the original number, then the original number is

[(11M - N)/2].

**Calculation:**

Here, M = 14 and N = 36

Required number = [(11 × 14) - 36]/2

⇒ (154 - 36)/2

⇒ 59

**∴ The Original number is 59.**

__Important Points__

If the sum of the digits of a two digit number is M. The number formed by reversing the digits is N less than the original number, then the original number is

[(11M + N)/2].