Question

a number consists of two digits whose sum is 9.if 27 is subtracted from the original number, its digits are interchanged. find the original number.​

Answer 1

Answer:

Original number is 63.

Step-by-step explanation:

Let the number of unit place is y

and number on tens place is x

Then the number is: 10x + y

Now, According to the question,

x + y = 9    → (1)

and 10x + y -27 = 10y + x

⇒ 9x - 9y = 27

⇒ x - y = 3    → (2)

Solving equation (1) and (2)

we get, x = 6 and y = 3

So the original number is 10x + y = 10 × 6 + 3 = 63

Answer 2

Answer :- 63

Let the Ones Digit of the Number be a and, Tens Digit be b.

• Required Number = (10b + a)

• After Interchanging = (10a + b)

As Per Question :

» a + b = 9

» a = 9 - b —(¡)

Given:

• If 27 is subtract from the original number its digits are interchange.

⇒ 10b + a - 27 = 10a + b

⇒ 10b + a - 27 - 10a - b = 0

⇒ 9b - 9a - 27 = 0

Dividing Each term by 9

⇒ b - a - 3 = 0

⇒ b - (9 - b) - 3 = 0 —( from ¡ )

⇒ b - 9 + b - 3 = 0

⇒ 2b - 12 = 0

⇒ 2b = 12

Dividing Each term by 2

⇒ b = 6

• Putting Value of b = 6 in (¡)

⇒ a = 9 - b

⇒ a = 9 - 6

⇒ a = 3

➙ Original Number

➙ (10b + a)

➙ (10 × 6 + 3)

➙ (60 + 3)

➙ 63

჻ Required Number is 63.