The total number of three-digit numbers, with one digit repeated exactly two times, is

 Number of three digit numbers in which  0 is taken twice  =9

{100,200,...900}

Number of three digit numbers in which  0 is taken once=  ${}^{9}C_1\times 2=18$

{101,110..........909,990}

Number of three digit numbers which do not contain  0 and  one nonzero digit is repeated (twice) ${}^{9}C_1{}^{8}C_1·3=216$

Total =243