Question

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

Answer 1

Let 2 digits of the number be x and y

According to the question,

x + y =  10   → → → [Equation 1]

Original Number ➜ 10x + y

On Reversing ➜ 10y + x

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

⇒ 10x + y - 36 = 10y + x

⟶  10x - x - 36 = 10y - y

⟶  9x - 36 = 9y

⟶  9x - 9y = 36

⟶  9(x - y) = 36

⟶  x - y = 36 ÷ 9

⇒ x - y = 4  → → → [Equation 2]

Adding Equations 1 and 2,

                 x + y = 10

            {+}  x - y = 4  

                2x = 14

⇒ x = 14 ÷ 2

⇒ x = 7

Substitute value of x in any one of the Equations to get the value of y.

x + y = 10

⇒ 7 + y = 10

⇒ y = 10 - 7

⇒ y = 3

Original Number

= (10x + y)

= 10(7) + 3

= 70 + 3

= 73

∴ The required Number = 73