Question

The sum of the digists of a two digit number is 12. The number formed by interchanging the digits is greater than the original number by 54. Find the original number.​

Answer 1

let X be the tens place number and Y be the ones place number

original number = 10 X + Y

according to condition 1

X + Y = 12 eq. 1

interchange number = 10 Y + x

according to condition 2

10y + X = 10 X + Y + 54

10 Y - Y + X - 10x = 54

9y - 9 x = 54

9(y-x)=54

y-x=54÷9

y-x=6 eq.2

add eq.1 and eq.2

x+y=12

+ -x+y=6

2y=18

2y=18

y=18÷2

y=9

put y=9 in eq.1

x+y=12

x+9=12

x=12-9

x=3

original number = 10x+y

=10×3+9

=30+9

=39

The original number is 39.