a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?
"now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 15 % profit . this means the clocks ' selling price was c ( 1.15 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 45 % the price at which the collector bought it . thus , you get = 1.15 * 0.45 * c = 0.5175 c furthermore , the store sells the clock for the second time for 85 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.85 = 1.85 * 0.5175 c finally given that c - 0.5175 c = 80 - - - - > c = 165.80 $ thus , the cost of the clock the second time around = 1.85 * 0.5175 c = 1.85 * 0.5175 * 165.80 = 158.74 $ . hence c is the correct answer ."
divide(multiply(80, divide(multiply(add(80, 85), divide(add(80, 15), const_2)), 80)), subtract(divide(add(80, 15), const_2), 15))