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:

Answer 1

Let the unit digit be x
and tens digit be y

The two digit number is :- 10y + x

• product of the digit is 27

xy = 27 .... ( i )



• If 54 is added to the number. the digit interchange their place.

54 + 10y + x = 10x + y

10y - y + x - 10x + 54 = 0

9y - 9x + 54 = 0

( dividing by 9 )

y - x + 6 = 0

y = -6 + x ..... ( ii )

Putting the value of y in equation ( i )

xy = 27

x ( -6 + x ) = 27

-6x + x² = 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 the value of x as 9 in equation ( ii )


y = - 6 + x

y = - 6 + 9

y = 3


The required number is

10y + x

10 × 3 + 9

30 + 9

39