Question

The sum of digits of 2 digit number is 14.if it get reveresed then the new number is 18 less than the original number.find the both number

Answer 1

Answer:

86

Step-by-step explanation:

Let the required number be  ab.

  All the two digit numbers can also be written as 10a + b, if number is ab.

Given,

  Sum of digits = 14

       ⇒ a + b = 14

       ⇒ a = 14 - b

When digits are reversed, new number is 18 less than the original. New number is ba which can be written as 10b + a.

According to the question:

⇒ 10a + b - 18 = 10b + a

⇒ 10a - a - 18 = 10b - b

⇒ 9a - 18 = 9b

⇒ a - 2 = b

⇒ a - b = 2

   From above, a = 14 - b

⇒ 14 - b - b = 2

⇒ 14 - 2b = 2

⇒ 14 - 2 = 2b

⇒ 12 = 2b

⇒ 6 = b

           Hence,

                    a = 14 - b

                       = 14 - 6

                       = 86

Required number is 86