Question

the sum of the digits of a 2 digit number is 7. If the digits are reversed the new number is equal to 3 less than 4 times the original number .Find the number

Answer 1

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
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Answer 2

The original number is 16.