A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?10202125
Question
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?10202125
Solution
Let's solve this step by step:
Step 1: Let's assume the initial volume of the mixture in the can is 'V' litres. According to the problem, the ratio of liquids A and B in the can is 7:5. So, the volume of liquid A in the can is 7V/12 and the volume of liquid B is 5V/12.
Step 2: 9 litres of the mixture is drawn off. The ratio of liquids A and B in the mixture that is drawn off would also be 7:5. So, the volume of liquid A in the drawn off mixture is 79/12 = 5.25 litres and the volume of liquid B is 59/12 = 3.75 litres.
Step 3: After drawing off 9 litres of the mixture, the volume of liquid A left in the can is 7V/12 - 5.25 and the volume of liquid B is 5V/12 - 3.75.
Step 4: The can is then filled with liquid B, so the volume of liquid B becomes 5V/12 - 3.75 + 9.
Step 5: After this, the ratio of liquids A and B becomes 7:9. So, we can write the equation as (7V/12 - 5.25) / (5V/12 - 3.75 + 9) = 7/9.
Step 6: Solving this equation, we get V = 21 litres.
Step 7: So, the initial volume of liquid A in the can was 7V/12 = 7*21/12 = 12.25 litres.
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