A can contains a mixture of two liquids x and y in the ratio 7:5. when 9 litres of mixture are drawn off and the can is filled with y the ratio of x and y becomes 7:9. how many litres of liquid x was contained by the can initially?
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A:B = 7:5
Total = 12 units
When 9 litres of mixture is removed, ((7/12) * 9) litres of A is removed, and ((5/12) * 9) litres of B is removed
Then 9 litres of B is added so that new ratio is 7:9
In new mixture, Total volume of A is 7x - ((7/12) * 9) = 7x - 21/4
And total volume of B is 5x - ((5/12) * 9) + 9 = 5x - 3 3/4 + 9 = 5x + 21/4
So, (7x - 21/4)/(5x + 21/4) = 7/9
Solving for x:
x=3
Original Volume of A = 7x = 21
Total = 12 units
When 9 litres of mixture is removed, ((7/12) * 9) litres of A is removed, and ((5/12) * 9) litres of B is removed
Then 9 litres of B is added so that new ratio is 7:9
In new mixture, Total volume of A is 7x - ((7/12) * 9) = 7x - 21/4
And total volume of B is 5x - ((5/12) * 9) + 9 = 5x - 3 3/4 + 9 = 5x + 21/4
So, (7x - 21/4)/(5x + 21/4) = 7/9
Solving for x:
x=3
Original Volume of A = 7x = 21
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