Question

the sum of the digit of a two digit number is 13. if 9 is added to the number digit are reversed find the original number

Answer 1

Answer:—

• 67

Step-by-step explanation:—

Let the number be denoted as 10x + y

⇒ x + y = 13 _________(1)

⇒ 10x + y + 9 = 10y + x

⇒ 10x - x + y - 10y = -9

⇒ 9x - 9y = -9

⇒ x - y = -1 ___________(2)

Adding ( 1 ) and ( 2 ) we get,

⇒ 2x = 12

⇒ x = 6

Substituting this in 1 we get,

⇒ 6 + y = 13

⇒ y = 13 - 6

⇒ y = 7

Hence,

The original number is 10x + y, which is:

⇒ 10 ( 6 ) + 7

⇒ 60 + 7

⇒ 67

Hence the original number is 67.

$\:$