Question

4. The sum of the digits of a 2-digit number is 8. If the digits are interchanged the number obtained
18 more than the original number. What is the original number?
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Answer 1

Let the 2 digits of the number be x and y

According to the question,

x + y = 8     →  →  → [Equation 1]

Original number ➜ (10x + y)

On reversing, ➜ (10y + x)

According to the question,

(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 Equations 1 and 2,

                    x + y = 8

           {+}   -x + y = 2

2y = 10

⇒ y = 10 ÷ 2

⇒ y = 5

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

x + y = 8

⇒ x + 5 = 8

⇒ x = 3

We know that Original Number = (10x + y)

= 10(3) + 5

= 30 + 5

= 35

∴ The Required number is 35

Confused? Let's Verify

• 3 + 5 = 8
• 53 = 18 + 35