Question

Product of digits of a 2-digit 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. options: 1) 39 2) 93 3) 63 4) 36

Answer 1

Let the unit digit be x
and tens digit be y

xy = 27 ... ( i )

10y + x + 54 = 10x + y

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

9y - 9x = - 54

y - x = - 6

y = x - 6 .... ( i )









xy = 27

x ( x - 6 ) = 27

x² - 6x - 27 = 0

x² - 9x + 3x - 27 = 0

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

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

• ( x + 3 ) = 0

x = - 3 [ Neglected ]

• ( x - 9 ) = 0

x = 9

Putting value of x in ( ii )

y = x - 6

y = 3

The required number is 10y + x

i.e, 36


So, option ( 4 ) 36 is ryt !!