Question

If the sum of digits of a two-digit number is 17. On reversing its digits, the new number is 9 more than the original number, then the number is

(a) 89 (b) 98
(c) 97 (d) 79​

Answer 1

Answer:(a) 89

Step-by-step explanation:

let the two digit number be xy

                        10x+y=xy          

reversed no be yx

                        10y+x=yx

x+y=17       → (1)

9+(10x+y) = 10y+x

9+(10x-x)+(y-10y)=0

9+9x-9y=0

divide (÷) the whole equation by 9

1+x-y=0

x-y=-1      → (2)

(1)+(2)    →→→→→→→           x + y = 17

                                       x  - y = -1

                                       2x      = 16  

        ∴ x=8        

substitute x in (1)

          8+y=17

              y=17-8

             y=9

∴the two-digit number is (A)89