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Two barrels of 25 liters and 40 liters respectively are filled with the mixture of milk and water in the proportion of 12 : 5 and 14 : 7. If 75% amount of the barrels is transferred to a tank which is filled with 15 liters of milk and 7 liters of water, then the proportion of water to milk in the mixture contained in the tank is?

Two barrels of 25 liters and 40 liters respectively are filled with the mixture of milk and water in the proportion of 12 : 5 and 14 : 7. If 75% amount of the barrels is transferred to a tank which is filled with 15 liters of milk and 7 liters of water, then the proportion of water to milk in the mixture contained in the tank is? Correct Answer 2251/4824

Available proportion in the tank = 15 litres of milk : 7 litres of water = 15 : 7

Total quantity available in tank = (15 + 7) litres = 22 liters

To find the amount of mixture added from first barrel :

Total amount available in first barrel = 25 liters

Amount added to tank = 75% of total amount

⇒ 75% of 25 = (75/100) × 25 = 18.75 litres

Amount of milk in the added mixture = (12/17) × 18.75 = 13.235 litres = 13.24 litres (approx.)

Amount of water in added mixture = 18.75 - 13.24 = 5.51 liters

To find the amount of mixture added from second barrel :

Total amount available = 40 liters

Amount added to tank = 75% of total amount = 75% of 40 = (75 × 40)/100 = 30 liters

Amount of milk in the added mixture = (14/21) × 30 = 20 liters

Amount of water in added mixture = 30 - 20 = 10 liters

Total amount of milk available in prepared mixture = 15 + 13.24 + 20 = 48.24 liters

Total amount of water available in prepared mixture = 7 + 5.51 + 10 = 22.51 liters

∴ Required ratio = (amount of water)/(amount of milk) = 2251/4824

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