Question

The sum of digits of a two-digit number is 10. When the digits are reversed, the number decreases by 54. Find the changed number.

• A. 73
• B. 28
• C. 82
• D. 37

Answer 1

Answer:

B. 28

Let the number be $10x+y$

when the digits are reversed the number is decreased by 54

$(10x+y)-54=10y+x$

$10x+y-10y-x=54$

$9(x-y)=54$

$x-y=6$

$x+y=10$

From this we get $x=8, y=2$

Number$= 28$