Question

the sum of the digits of a number is 13 and the difference between the number and that formed by reversing the digits is 27 find the number?

Answer 1

Hello Friend !

Since it is a two digit number, therefore let the number be :- xy i.e., 10x + y .

Therefore, according to t⇒he question, x + y = 13  .........[ eq. 1 ]

When the digits are reversed, the number becomes yx i.e., 10y + x .

Also, as given in the question, the difference between the number and the reversed number is = 27

Mathematically,

(10x + y ) - ( 10y + x ) = 27

⇒ 10x + y - 10y - x = 27 

⇒ 9x - 9y = 27

Dividing both sides by 9 

⇒ x - y = 3 ...........[ eq. 2 ]

Adding eq. 1 and eq. 2 , we get ,

⇒ x + y + x - y = 13 + 3 

⇒ 2x = 16

⇒ x = 8

Substituting x = 8 in eq. 1 , we get,

⇒ y = 13 - 8

⇒ y = 5

Therefore, the original number is 10x + y i.e., 10×8 + 5 = 85.

This is your answer.

Hope this HELPS !!!