5. A container contains a mixture of two liquids P and Q in the ratio of 7:5. When 9 liters of mixture is taken out and replaced with Q, the ratio becomes 7:9. Find the quantity of liquid P in the container.*100 liters200 liters524 liters252 liters
Question
5. A container contains a mixture of two liquids P and Q in the ratio of 7:5. When 9 liters of mixture is taken out and replaced with Q, the ratio becomes 7:9. Find the quantity of liquid P in the container.*100 liters200 liters524 liters252 liters
Solution
Let's solve this step by step:
Step 1: Let's assume the total quantity of the mixture in the container is T liters. According to the problem, the mixture contains liquids P and Q in the ratio 7:5. So, the quantity of P = (7/12)*T and the quantity of Q = (5/12)*T.
Step 2: 9 liters of this mixture is taken out. So, the quantity of P and Q taken out will be in the same ratio of 7:5. Therefore, quantity of P taken out = (7/12)*9 = 5.25 liters and quantity of Q taken out = (5/12)*9 = 3.75 liters.
Step 3: This 9 liters is replaced with 9 liters of Q. So, the new quantity of P = (7/12)*T - 5.25 and the new quantity of Q = (5/12)*T - 3.75 + 9.
Step 4: According to the problem, this new mixture is in the ratio 7:9. So, ((7/12)*T - 5.25)/((5/12)*T - 3.75 + 9) = 7/9.
Step 5: Solving this equation, we get T = 252 liters. So, the quantity of liquid P in the container = (7/12)*252 = 147 liters.
So, none of the options given in the question is correct. The correct answer should be 147 liters.
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