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Reversing the 3 Digit Numbers and Subtracting Them

A two-digit n...

Question

A two-digit number becomes five-sixth of itself when its digits are reversed. The two digits differ by one. What is the number?

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Solution

Let the number be $= 10 a + b$

$10 b + a = \frac{5}{6} (10 a + b), a n d a - 1 = b, 5 (10 a + a - 1) = 6 (10 a - 10 + a) 55 a - 5 = 66 a - 60, 11 a = 55, a = 5, b = 4$

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