Question

The sum of the digits of a two digit number is 8.If 18 is added to the value of the number,

its digits get reversed. Find the number detail q stion

. ​

Answer 1

If 18 is added to the number, the digits change their places. Hence, the number is 35.

Step-by-step explanation:

Let the number be in the form of 10x+y, where x and y are the tens digit and the units digit respectively.

Applying the first condition:, we get

x+y=8 ....(1)

Applying the second condition, given in the problem

10x+y+18=10y+x

⇒9x−9y=−18

⇒x−y=−2 ....(2)

By solving equations (1) and (2), we get

x=3 and y=5

Therefore, 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