In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: given a two - digit number , the unit ' s digit exceeds its 10 ' s digit by 5 and the product of the given number and the sum of its digits is equal to 90 , which of the options is the number ?
Options: a ) 27 , b ) 16 , c ) 38 , d ) 61 , e ) 83
a