Question

The product of the digits of a two-digit number is twice as large as the
sum of its digits. If we subtract 27 from the required number, we get a
number consisting of the same digits written in the reverse order. Find
the number.

Help Me Plz​

Answer 1

Let x and y be the two digits

such that 10x+y is the number.

According to question xy= 2(x+y)

x= 2(x+y)/y (1)

And again,

10x+y-27= 10y+x

9x-9y= 27

x= 3+y (2)

On equating (1) and (2)

3+y= 2(x+y)/y

(3+y)y=2x+2y

3y+y²=2(3+y) +2y

y²+3y-2y=6+2y

y²+y-2y-6= 0

y²-y-6=0

y²+2y-3y-6=0

y(y+2)-3(y+2)=0

so either y= -2 or y= 3

y=-2 is not possible as x will be 1 making them negative while deducting 27 from it,

So,

when y = 3

x= 3+y= 3+3= 6

so the number is 10x+y= 10×6+3= 63