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.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
