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