Quantity I: A mixture of milk and honey, ratio 9:4, is put in a vessel. 26 liters of honey are added to the 65 liters of mixture that were previously in the vessel, making the ratio of milk to honey in the vessel 7:6. Determine how much mixture was initially in the vessel. Quantity II:  Pipes P and Q together can fill an empty tank in 24 minutes. Pipe P alone can fill the tank in 15 minutes. Find the capacity of the tank if pipe Q alone can pump out 4 litres of water in one minute.

ATQ, Quantity I: Let the initial quantities of milk and honey in the vessel be 9a litre and 4a litres, respectively. 65 litres mixture contains 45 litres milk and 20 litres honey So according to question:  (9a – 45)/ (4a – 20 + 26) = 7/6 54a – 270 = 28a + 42 26a = 312,  a = 12 So, the initial quantity of mixture in the vessel = 12 × 13 = 156 litres Quantity II: Let the capacity of the tank = 120a litres So, the quantity of water filled by pipes P and Q together in one minute = 120a/24 = 5a litres Quantity of water filled by pipe P alone in one minute = 120a/15 = 8a litres Quantity of water taken out by pipe Q alone in one minute = 8a – 5a = 3a Time taken by pipe Q alone to empty the full tank = 120/3a = 40 minutes So, the capacity of the tank = 4 × 40 = 160 litres So, Quantity I < Quantity II