Question

The sum of digits of a two-digit number is 10. The difference between the number and the number obtained by reversing the digits is 18. Find the appropriate equations.

• A. x+y = 10 ; 2x +y =11
• B. x +y =10; x + y = 10
• C. x + y =11 ; y +2x =11
• D. x + 2y = 10 ; 2x + y = 11

Answer 1

The correct option is B

x +y =10; x + y = 10

Let $x$ represent the tens digit and $y$ represent the units digit.

Then, the two-digit number can be expressed as $10x+y$
From question, we have $x+y=10$
If the original number is $10x+y$, then the number obtained by reversing its digits is $10y+x$.
Given that $10x+y-10y-x=18$

$\Rightarrow 9x-9y=18$

$\Rightarrow x-y=2$