there are 5 thieves , each loot a bakery one after the other such that the first one takes 1 / 2 of the total no . of the breads plus 1 / 2 of a bread . similarly 2 nd , 3 rd , 4 th and 5 fth also did the same . after the fifth one no . of breads remained are 3 . initially how many breads were there ?  Choose the correct choice from the following answers.
A) 124  B) 125  C) 126  D) 127  E) 128

Rationale: let the number of breads initial be x you should go in reverse order as left bread is 3 i . e x = ? after 1 st person ate a = x - ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - x ) / 2 - ( 1 / 2 ) i . e a = ( x / 2 ) - ( 1 / 2 ) i . e a = ( 2 x - 2 ) / 4 i . e a = ( x - 1 ) / 2 like wise - - - - after 2 nd person ate b = ( a - 1 ) / 2 like wise - - - - after 3 rd person ate c = ( b - 1 ) / 2 like wise - - - - after 4 th person ate d = ( c - 1 ) / 2 like wise - - - - after 5 th person ate e = ( d - 1 ) / 2 now as after 5 th person ate the value of remaining bread is - - - 3 therefore the value of e = 3 ; now go reverse from botom to top to get the value of x after calcuating value of d = 7 value of c = 15 value of b = 31 value of a = 63 value of x = 127 so the final answer is 127 breads were there answer : d
Answer: D