Question

11. The sum of the digits of a two-digit number is 12. The number obtained
by interchanging its digits exceeds the given number by 18. Find the
number.
[CBSE 2006)​

Answer 1

Let 2 digit number be x and y

According to the Question,

The sum of 2 digit number is 12

⇒ x + y = 12       ⟶  ⟶  ⟶ [Equation 1]

Original Number: 10x + y

On interchanging the digits; 10y + x

Now,

(10y + x) = 18 + (10x + y)

⇒ 10y + x = 18 + 10x + y

⇒ 10y - y = 18 + 10x - x

⇒ 9y = 18 + 9x

⇒ 9y - 9x = 18

⇒ 9(y - x) = 18

⇒ (y - x) = 18 ÷ 9

⇒ (y - x) = 2       ⟶ ⟶ ⟶ [Equation 2]

Adding Equation 1 and 2,

                x + y = 12

        {+}    -x + y = 2

                       2y = 14

→ 2y = 14

→ y = 14 ÷ 2

∴ y = 7

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

x + y = 12

⇒ x + 7 = 12

⇒ x = 12 - 7

∴ x = 5

Now, let's find the number.

Original Number = 10x + y

→ Original Number = 10(5) + 7

→ Original Number = 50 + 7

∴ Original Number = 57