Question

a number consists of two digits whose sum is 8 if 18 is added to the number of its digit are reversed find the answer​

Answer 1

Let the -

• ten's digit number be M
• one's digit number be N

Sum of numbers is 8.

According to question

⇒ M + N = 8 ___ (eq A)

⇒ M = 8 - N __ (eq 1)

If 8 is added to the number the digits got reversed.

Now,

• Original number = 10M + N
• Revered number = 10N + M

According to question

⇒ 10N + M = 10M + N + 18

⇒ 10N - N + M - 10M = 18

⇒ 9N - 9M = 18

⇒ N - M = 2

⇒ N - (8 - N) = 2

⇒ N - 8 + N = 2

⇒ 2N = 10

⇒ N = 5

Substitute value of N = 5 in (eq 1)

⇒ M = 8 - 5

⇒ M = 3

•°• Original number = 10M + N

⇒ 10(3) + 5

⇒ 30 + 5

⇒ 35

Verification :-

From above calculations we have M = 3 and N = 5

Substitute value of M and N in (eq A)

→ 3 + 5 = 8

→ 8 = 8

Answer 2

Answer:

Let the digits be represented as 'x' and 'y' such that 'x' is in unit's place and 'y' is in ten's place.

According to the question,

• x + y = 8
• 10y + x + 18 = 10x + y

From the first equation we get,

⇒ x = 8 - y

Substituting this in the second equation we get,

⇒ 10y + 8 - y + 18 = 10 ( 8 - y ) + y

⇒ 9y + 26 = 80 - 10y + y

⇒ 9y + 26 = 80 - 9y

⇒ 9y + 9y = 80 - 26

⇒ 18y = 54

⇒ y = 54/18

⇒ y = 3

Substituting the value of 'y' in first equation we get,

⇒ x + 3 = 8

⇒ x = 8 - 3

⇒ x = 5

According to our assumption y is in the terns place and x is in the one's place. Hence the number is 35.