Question

The sum of the digits of a two digit numben is 13.
if 9 is added to the number, the digits are
reversed. Find the orginal number.​

Answer 1

Whatever the condition is given, Let us first assume the ones and tens digits of the given two-digit number to be y and x respectively.

Condition 1st :-

The sum of the digits of the given two-digit number is 13.

Since we assumed the digits to be x & y.

∴ x + y = 13 ...[1]

Condition 2nd :-

If 9 is added to the given number, The digits get reversed.

First of all, A two digit number is of the form n + 10m , where

• n = One's digit
• m = Ten's digit

So, According to this, the number we assumed would be 10x + y

And the number obtained after adding 9 to the given number we get 10y + x (Digits get reversed)

∴ Original Number + 9 = Obtained number

⇒ 10x + y + 9 = 10y + x

⇒ 9x - 9y = -9

⇒ x - y = -1 ...[2]

Now, that we have two equations, we can easily find the value of x and y, Adding [1] & [2]

⇒ x + y + x - y = 13 - 1

⇒ 2x = 12

⇒ x = 6

Substituting the value of x in [1]

⇒ 6 + y = 13

⇒ y = 7

So we have finally got the values of x and y.

Substituting the value of x and y, we get

⇒ Original Number = 67

Answer 2

Answer:

Original number is 67.

Step-by-step explanation:

Assume that the ten's digit number be x and one's digit number be y.

The sum of the digits of a two digit numben is 13.

As per given condition,

→ x + y = 13

→ x = 13 - y ...............(1)

If 9 is added to the number, the digits are reversed.

• Original Number = 10x + y
• Reversed Number = 10y + x

As per given condition,

→ 10x + y + 9 = 10y + x

→ 9x - 9y = - 9

→ x - y = -1

→ 13 - y - y = - 1 [From (1)]

→ 2y = 14

→ y = 7

Substitute value of y in (1)

→ x = 13 - 7

→ x = 6

Hence, the original number = 10x + y = 67.