Question

the sum of the digits of a two digit number is 8 . If number firmed by reversing the digits is less than the original no. by 18 find the original number. option 1)53 2)54 3)55 4)56 .​

Answer 1

Answer:

Step-by-step explanation:

Let the two digit number be xy

 x + y = 8

Now algebraically:

⇒ x + y = 8  --------------- (i)

 

The value of xy is 10x + y

The value of yx is 10y + x

 

⇒ 10y + x = 10x + y + 18  

⇒ 9y - 9x = 18

⇒ 9(y - x) = 18

⇒ y - x = 2

 

From equation 1: y = 8-x

 

⇒ 8 - x - x = 2

⇒ 8 - 2x = 2

⇒ -2x = -6

⇒ x = 3

 

⇒ y - x = 2

⇒ y - 3 = 2

⇒ y = 5

 

Hence, Original number xy = 35