There are two vessels A and B. Vessel A contains 25 liters of pure milk and vessel B contains 15 liters of pure water. Five liters of milk is taken out from vessel A and poured into vessel B. Then, 5 liters of mixture is taken out from vessel B and poured into vessel A. What is the ratio of the quantity of pure milk in vessel A to the quantity of water in vessel B
Question
There are two vessels A and B. Vessel A contains 25 liters of pure milk and vessel B contains 15 liters of pure water. Five liters of milk is taken out from vessel A and poured into vessel B. Then, 5 liters of mixture is taken out from vessel B and poured into vessel A. What is the ratio of the quantity of pure milk in vessel A to the quantity of water in vessel B
Solution
Step 1: Initially, vessel A has 25 liters of pure milk. When 5 liters of milk is taken out, it is left with 20 liters of milk.
Step 2: Vessel B initially has 15 liters of pure water. When 5 liters of milk is added, it now contains 15 liters of water and 5 liters of milk.
Step 3: Now, 5 liters of the mixture from vessel B is taken out and poured into vessel A. This mixture contains both milk and water. Since the mixture in vessel B is 1/4 milk (5 liters out of 20 liters) and 3/4 water, the 5 liters taken out would also be 1/4 milk and 3/4 water. So, 1.25 liters of milk and 3.75 liters of water are removed from vessel B.
Step 4: The 5 liters of mixture added to vessel A contains 1.25 liters of milk and 3.75 liters of water. So, vessel A now contains 21.25 liters of milk (20 liters + 1.25 liters) and 3.75 liters of water.
Step 5: Vessel B is now left with 3.75 liters of milk (5 liters - 1.25 liters) and 11.25 liters of water (15 liters - 3.75 liters).
So, the ratio of the quantity of pure milk in vessel A to the quantity of water in vessel B is 21.25:11.25 or 85:45 when simplified.
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