Answer:

Step-by-step explanation:

• Reversing the digits, the number obtained is 9 less than 3 TIMES the original umber
• Difference of these two numbers = 45

• The original number

→ Let the ten's digit be x

→ Let the unit's digit be y

→ HENCE the number would be 10x + y

→ Reversing the number,

  Reversed number = 10y + x

→ By given

  10y + x = 3 (10x + y) - 9

  10y + x = 30X + 3y - 9

  10y -3y = 30x - x - 9

   7y = 29 x - 9

   29x - 7y - 9 = 0 ------(1)

→ Also by given

  10y + x - (10x + y) = 45

  10y + x -10x - y =45

   9y - 9x = 45

→ Dividing the whole equation by 9

   y - x = 5

   y = 5 + x ----(2)

→ Substitute equation 2 in equation 1

   29x - 7(5 + x) - 9 = 0

   29x - 35 - 7X - 9 = 0

   22X - 44 = 0

   22x = 44

       x = 44/22

       x = 2

→ Hence the ten's digit is 2

→ Substitute the value of x in 2

  y = 5 + 2

  y = 7

→ The unit's digit is 7

→ Hence the number is 2 × 10 + 7

  The number = 20 + 7

  The number = 27

→ By the first case,

  10y + x = 3 (10x + y) -9

  10 × 7 + 2 = 3 (10 × 2 + 7) - 9

  70 + 2 = 3 ( 20 + 7) -9

  72 = 3 ( 27) - 9

  72 = 81 - 9

  72 = 72

→ Difference of the reversed and orginal number = 45

  10y + x - (10x + y) = 45

  10 × 7 + 2 - (10 × 2 + 7) = 45

  70 + 2 - (20 + 7) = 45

  72 - 27 = 45

  45 = 45

→ Hence verified.