The difference of the digits of a two-digit number is 7. If the digits are reversed, the new number becomes 9/2 times the original number. Find the number.
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Let the two digit number is represented by xy.Given x + y = 9 when the digits are reversed we get yx. Now yx can also be written as 10y + x since y corresponds to 10th place and x corresponds to unit place.
xy = 10x + y
given 10y + x -10x -y = 9
=> - 9x +9y = 9
=> -x + y = 1. We also know x + y = 9
solving the above equations we get x = 4 and y = 5
=> the number is 45 which when reversed become 54 that is increased by 9.
Hence the digit is 45.
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Answer:
the correct answer is 5
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