Question

the sum of the digits of a two digit number is 7 . if the digits are reversed , the new number increased by 3equal 4times the original number .find the original number​

Answer 1

⊕ANSWER⊕

Let the digits be x and y... and so, the original number be 10x + y ( since x in tenth place and y in unit place)

so, given : sum of the digits = x + y = 7 ---------> (A)

                 

reversing the digits means y in tenth place and x in unit place.. so, the reversed number be 10y + x

        

  given: reversed number is decreased by 2 = twice original number

 

         so, 10y + x - 2 = 2(10x + y) 

          simplifying :   19x - 8y = -2       ------------> (B)

solving 2 eqns (A) & (B) ,

 we get x = 2 and y = 5

so the original number is 10x + y = 10(2) + 5 = 25

  & the reversed number is 10y + x = 10(5) + 2 = 52

   & the reversed number 52  when decreased by 2 is 50 which is twice the original number 25 

Ans: the original number is 25