Then: the original price is C/( 1-r)
The original profit is c/(1-r)-c = RC/(1-r) (original price-original cost).
The current price is (1+0.5) c/(1-r) =1.5c/(1-r) (1.5 * original price).
The current cost is c (1+10%) =1.1c (1.1* original cost).
The current profit is1.5c/(1-r)-1.1c (current price-current cost).
So1.5c/(1-r)-1.1c = 1.6 * RC (1-r) (current profit =1.
0.5r=0.4
The solution is r=0.8 (that is, 80%)