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?

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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#