Answers

1. Answer:

   75

   Step-by-step explanation:

   Let the unknown number be AB where A is the digit in the tens place and B the digit in the units place

   The actual value of the number is computed as 10A + 1B because the tens place has positional value of 10 and units place has positional value of 1

   We are given B = A – 2 or alternatively, A = B + 2

   The number reversed is BA which has the value 10B + A

   The second fact about the number is translated into the equation

   2(10A + B) – (10B + A) = 93

   Expanding the brackets we get

   20A + 2B -10B – A = 93

   Simplifying and collecting the unknowns on the LHS gives us

   19A – 8B =93

   Substitute A in terms of B where A = B + 2

   19(B+2) – 8B = 93

   19B + 38 – 8B = 93

   11B = 93-38=55

   So B = 55/11 = 5 and A = 5 + 2 = 7

   So the original number is 75

   We can verify this using the second fact

   Twice the original number = 2(75) = 150

   75 reversed is 57

   And we have 150-57 = 93

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