Question

the sum of the digits of a two digit number is 15. if the number formed by reversing the digits is less than the original number my 27, find the original number

Answer 1

         

Answer: 96

       

The difference of a two digit number and the number formed by interchanging the digits is 9 times the difference of the digits.

Let the no. be 10x + y.

So that the no. formed by interchanging digits is 10y + x.

x + y = 15     →     (1)

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

⇒ 9(x - y) = 27

⇒ x - y = 3     →     (2)

(1) + (2)

⇒ (x + y) + (x - y) = 15 + 3

⇒ 2x = 18

⇒ x = 9

(1) - (2)

⇒ (x + y) - (x - y) = 15 - 3

⇒ 2y = 12

⇒ y = 6

 

 

So,  10x + y = 10 × 9 + 6 = 90 + 6 = 96.

So 96 is the answer.

Hope this helps. Plz ask me if you've any doubts.

Thank you. :-))