Question

The sum of the digits of a two-digit number is 12. If the new number formed by reversing the

digits is greater than the original number by 54, find the original number. Check your solution.​

Answer 1

Answer:

Step-by-step explanation:

now x+y =12

y=12-x

now the number

10x+12-x

reversed number = 10(12-x)+x

now

120-9x=9x+12+54

120-66=9x+9x

54=18x

x=54/18

x=3

now original number =9x+12=27+12=39

Answer 2

Answer:

let the digits are x and y

so the number is 10x+y

again, x+y=12

by reversing the digits we get the new number 10y+x

so, 10y+x=10x+y+54

=> 10y+x-10x-y=54

=> 9y-9x=54

=> 9(y-x)=54

=> y-x=54/9=6

=> y=6+x

x+y=12

=> x+6+x=12

=> 2x=12-6

=> 2x=6

=> x=6/2

=> x=3

y=6+x=6+3=9

so the original number is 10x+y

=10×3+9

=30+9

=39