A rectangular tiled patio is composed of 160 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 160 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?  Choose the correct choice from the following options:  A) 5  B) 6  C) 10  D) 13  E) 28

Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 160 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 160 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 160 ( 2 r - 4 ) * r = 160 2 r ^ 2 - 4 r - 160 = 0 r can not be negative so r = 10 and c = 16 so , answer will be c"
Answer: C