Question : The sum of the digits of a two-digit number is 10. The number formed by reversing the digits is 18 less than the original number. Find the original number.
Option 1: 81
Option 2: 46
Option 3: 64
Option 4: 60
Correct Answer: 64
Solution : Let the digit in one's place of the number be $x$ and the digit in ten's place be $y$. So number = 10$y$ + $x$ By reversing that number = 10$x$ + $y$ According to the question, $x$ + $y$ = 10 --------- (1) So, $x$ + 10$y$ – 18 = 10$x$ + $y$ ⇒ $x$ + 10$y$ – 10$x$ – $y$ = 18 ⇒ –9$x$ + 9$y$ = 18 ⇒ –9($x$ – $y$) = 18 ⇒ ($x$ – $y$) = –2 -----------(2) By adding equation(1) and (2), we get, ⇒ 2$x$ = 8 ⇒ $x$ = 4 Put value of x in equation(1), ⇒ $y$ = 6 So, number = $x$ + 10$y$ = 4 + 10 × 6 = 64 Hence, the correct answer is 64.
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