Question

A no.consist of two digit whose product is 18. when 27 is subtracted from the no, the digits change place

Answer 1

Let the unit digit be x
and ten's digit be y


Original number :- 10y + x


as product of numbers is 18

then, xy = 18


x = 18 / y .....( i )



Now,

When 27 is subtracted from the number the number changed it's place

So ,

10y + x - 27 = 10x + y


10y - y + x - 10y - 27 = 0

9y - 9x - 27 = 0

y - x - 3 = 0 ...... ( ii )


Putting value of x from ( i ) in ( ii )
we get,


y - x - 3 = 0

y - ( 18/y ) - 3 = 0


$\frac{ {y}^{2} - 18 - 3y}{y} = 0$

( by sending y to 0 we get 0 )



y² - 18 - 3y = 0

y² - 3y - 18 = 0

y² - 6y + 3y - 18 = 0


y ( y - 6 ) + 3 ( y - 6 ) = 0

( y + 3 ) ( y - 6 ) = 0


=> ( y + 3 ) = 0

y = -3


=> ( y - 6 ) = 0

y = 6



If y = -3

then,

x = 18/y

x = 18/ -3

x = -6

If y = 6

then,

x = 18/y

x = 18/6

x = 3


So, if we have taken negative number
then number is,

10y + x

= 10 × ( -3 ) + ( - 6 )

= -30 - 6

= -36


And,

If the number is positive
then,

10y + x

= 10 × 6 + 3

= 60 + 3

= 63

@Altaf