# The sum of the two-digit number is 9. When we interchange the digits the new number is 27 greater than the earlier number. Find the number.

Let us find the number using the base-10 numeral system.

## Answer: The required two-digit number is 36.

Let's the digits in the number as x and y. Then the number is 10x + y. Let's proceed to find the number.

**Explanation:**

Let the required number be 10x + y.

Therefore, the given data can be decoded as:

- Sum of the digits is 9 ⇒ x + y = 9 --------------> equation (i)

The number obtained by interchanging the digits is 10y + x.

- New number = 27 + original number
- 10y + x = 27 + (10x + y)

⇒ 10y + x = 27 + 10x + y

⇒ 10y - y + x - 10x = 27

⇒ 9y - 9x = 27

y - x = 3 -----------> equation (ii)

By adding equation(i) and equation(ii):

x + y + y - x = 9 + 3

⇒ 2y = 12

⇒ y = 6

From equation(i): x + 6 = 9

⇒ x = 9 - 6 = 3

⇒ x = 3 and y = 6

therefore, the required number is 10x + y = 10 × 3 + 6 = 30 + 6 = 36