Question

2. 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.​

Answer 1

Let the digits be x and y, so the number will be = (10x+y), on reversing the digits, the new number will be = (10y+x)

According to the question we can write as x + y=12 and also we can write as 10y+x-10x-y=54

Which implies 9y-9x=54

y-x=54/9

y-x=6

y=6+x

Now on substituting this in x + y=12 we get x+6+x=12

2x+6=12

2x=12-6

x=6/2=3

Now y=6+x=6+3=9

So the number is 39

To check: digit sum=3+9=12

Reversing the digit numbers becomes 93 and 93-39=54

Hence verified.