Quantity I:  Boat 'P' travels 540 m downstream in 45 seconds, while boat 'Q' travels 240 m upstream in 48 seconds. If the ratio of the speed of boat P in still water to the speed of boat Q in still water is 19:15, find the time it takes for boat 'P' to cover 224 m upstream. Quantity II:  In a mixture of juice and water, the amount of juice exceeds the amount of water by 6 liters. The ratio of the cost of pure juice to the cost of the mixture is 5:3. If 5 liters of the mixture is replaced with the same quantity of juice, what will be the new cost of the mixture?

ATQ, Quantity I: Let the speeds of boats P and Q in still water are ‘19x’ m/s and ‘15x’ m/s respectively. Also let the speed of the stream is ‘y’ m/s. So, 19x+y= 540/45 19x + y = 12 ---------- (1) And 15x-y= 240/48 15x – y = 5 ---------- (2) From equations (1) and (2): x = 0.5, y = 2.5 Since, the upstream speed of boat P = 19 × 0.5 – 2.5 = 7 m/s So, the time, in which boat P can cover 224 m upstream = 224/7 = 32 seconds Quantity II: Let the initial quantity of water = ‘x’ L So, the initial quantity of juice = (x + 6) L Let the cost of pure juice is Rs.’5y’ per L and the initial cost of the mixture is Rs.‘3y’ per L. So, ((x+6)×5y)/(2x+6)=3y 5x + 30 = 6x + 18 x = 12 The initial quantity of water = 12 L The initial quantity of water = 12 L The initial quantity of juice = 12 + 6 = 18 L After replacing 5 L quantity of the mixture with the same quantity of juice: The new quantity of juice = 18 – 3 + 5 = 20 L The new quantity of water = 12 – 2 = 10 L Since, we don’t know the cost of the pure juice. So, the cost of new mixture can’t be determined. Hence, relation can’t be established