Question

Product of digits of a 2-digits number is 27. If we add 54 to the number, the new number obtained is a number formed by interchange of the digits. Find the number.


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Answer 1

Answer:

Let the number be xy=(10x+y)

A/Q;

x*y=27

=x=27/y

Now,

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

=10x+y+54=10y+x

=9x-9y+54=-

=9(x-y+6)=0

=x-y+6=0

=6=y-x --------(1)

=6=y-27/y

y^2-27-6y=0

(y+3)(y-9)=0

Therefore;

y=-3 and y=9

Since y!=0

Hence y=9

X=y-6  {from 1}

x=3

The number=10x+y=10*3+9=30+9=39