Question

In a two digit number the sum of the two digits is 8. If 18 is added to the number its digits are reversed. Find the number.

Answer 1

3 + 5 = 8

35 + 18 = 53

So the number is 35

Answer 2

• The number is 35

Step-by-step explanation:

Let,

• The tense digit be 'x'
• The Ones digit be 'y'
• The number be '10x + y' ------- (1)

According to the question,

x + y = 8

y = 8 - x -------- (2)

Solving,

⟼ 10x + y = 10x + (8 - x)

⟼ (10x - x) + 8

⟼ 9x + 8

Reversed number,

⟼ 10y + x = 10 (8 - x) + x

⟼ (80 - 8x) + x

⟼ 80 - 9x

When 18 is added to the number, its digits are interchanged,

⟼ (9x + 8) + 18 = 80 - 9x

⟼ 9x + 9x = 80 - 18 - 8

⟼ 18x = 54

⟼ x = 54 / 18

⟼ x = 3

Substituting 'x' in (2),

⟼ y = 8 - x

⟼ y = 8 - 3

⟼ y = 5

Substituting 'x' & 'y' in (1),

⟼ 10x + y

⟼ 10 (3) + 5

⟼ 30 + 5

⟼ 35

• The number is 35