Question

The sum of the digits of a two digits number is 10.if 36 is subtracted from the number ,the digits interchange their places . find the number .​

Answer 1

Let the 2 digits of the number be:

• x and
• y.

According to the question,

x + y = 10 ----- [Equation 1]

Original number → (10x + y)

On interchanging → (10y + x)

10x + y - 36 = 10y + x

⇒ 10x - x - 36 = 10y - y

⇒ 9x - 36 = 9y

⇒ 9x - 9y = 36

⇒ 9 (x - y) = 36

⇒ (x - y) = 4

⇒ x - y = 4 ----- [Equation 2]

Adding Equation 1 and 2,

x + y = 10

{+} x - y = 4

→ 2x = 14

→ x = 14 ÷ 2

→ x = 7

Substitute the value of y in Equation 1 to find out the value of x.

x + y = 10

⇒ 7 + y = 10

⇒ y = 3

The original number is (10x + y)

→ 10(7) + 3

→ 70 + 3

→ 73

∴ Original number = 73