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Tip #1: Assume that the productivity of each worker is constant Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? Solution: Let the total amount of work to be done be W units. Productivity of A, Pa = W/6 units per day. Productivity of B, Pb = W/8 units per day. 3 days x [Pa + Pb + Pc] = W =>Pc = W/24 units per day Ratio of wages of A : B : C = Ratios of their productivities = (W/6) : (W/8) : (W/24) = 4 : 3 : 1. Amount to be paid to C = Rs. 3200 x (1/8) = Rs. 400 Question: It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B used alone takes 8 hours to fill the same tank. We want to use three pumps: A, B and another pump C to fill the tank in 2 hours. What should be the rate of pump C? How long would it take pump C, used alone, to fill the tank? Solution: Let the total capacity of the tank be C liters. Fill rate of pump A, Fa = C/6 liters per hr Fill rate of pump B, Fb = C/8 liters per hr 2 hrs x [Fa + Fb + Fc] = C => Fc = 5C/24 liters per hr Let t be the time taken by only pump C to fill the tank. t hrs x 5C/24 = C => t = 24/5 = 4.8 hrs
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