A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. What is the number?

1 Answer
Apr 1, 2017

Number is #26#

Explanation:

Let the unit's digit in the number be #x#, then as product of digits is #12#, the ten's digit in the number is #12/x#.

Hence, the value of the number is #10xx12/x+x=120/x+x#

On reversing the digits, unit's digit becomes ten's digit and ten's digit becomes unit's digit and its value will become

#10x+12/x#

It is apparent that #10x+12/x# is greater than #120/x+x# by #36#

Hence #10x+12/x=120/x+x+36#

or #9x=(120-12)/x+36#

or #9x=108/x+36# and dividing each term by #9# we get

#x=12/x+4# and now multiply each by #x# to get

#x^2=12+4x# or #x^2-4x-12=0#

i.e. #x^2-6x+2x-12=0#

or #x(x-6)+2(x-6)=0#

i.e. #(x+2)(x-6)=0#

Hence, #x=-2# or #x=6#

But we cannot have negative number in units place

Hence, #6# is in unit's place and in ten's place we have #12/6=2#

and number is #26#