A two-digit number whose sum of digits is 14. If 36 is added to the number, the digts are interchanged. How do you find the number?

Question

18977 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-21T05:01:40

Number is #59#

Let the unit's digit be #x# as sum of digits is #14#, ten's digit is #14-x#,

then the number is #10xx(14-x)+x#

i.e. #140-10x+x# or #140-9x#

Reversing the digits number, unit digit becomes #14-x# and tens digit becomes #x#, hence number is #10x+14-x=9x+14#.

As adding #36# to #140-9x# makes it #9x+14#, we have

#140-9x+36=9x+14#

or #176-14=9x+9x#

or #18x=162#

or #x=9#

and hence, unit''s digit is #9# and tens digit is #5#

and number is #59#