In a two digit number, the units digit is twice the tens digit. If 18 is added to the number, the digits interchange their places. Find the number.


Answer:

24

Step by Step Explanation:
  1. Let the tens digit be x and the units digits be y. Then the number will be 10x + y.
  2. We are told that the units digit is twice the tens digit. This fact can be written as:
    y - 2x = 0 ________________________(1)
  3. We are also that if 18 is added to the number, the digit interchange their places. This fact can be written as:
    (10x + y) + 18 = 10y + x
    or, 9x - 9y = -18
    or, x - y = -2 ________________________(2)
  4. On adding the two equations (1) and (2),
    y - 2x + x - y = -2
    -x = -2
    x = 2
  5. y = 2x = 2 × 2 = 4
    Therefore, the number is 24.

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