A can contains a mixture of two liquids a and b in the ratio 7: 5. When 9 litres of the mixture isdrawn off and the can is filled with b, the ratio of a and b becomes 7: 9. How many litres ofliquid a was contained by the can initially?
Answers
Answer---->21
Explanation :Let’s initial quantity of P in the container be 7x
and initial quantity of Q in the container be 5x
Now 9 litres of mixture are drawn off from the container Quantity of P in 9 litres of the mixtures drawn off = 9×7/12=63/12 =21/4
Quantity of Q in 9 litres of the mixtures drawn off =9×5/12=45/12=15/4
Hence Quantity of P remains in the mixtures after 9 litres is drawn off =7-21/4
Quantity of Q remains in the mixtures after 9 litres is drawn off =5x-15/4
Since the container is filled with Q after 9 litres of mixture is drawn off,Quantity of Q in the mixtures =5x-15/4+9=5x+21/4
Given that the ratio of P and Q becomes 7 : 9
(7x-21/4) : (5x+21/4)=7:9
(7x-21/4)/(5x+21/4)=7/9
63x-(9×21/4)=35x+(7×21/4)
28x=(16×21/4)
x=(16×21)/(4×28)
litres of P contained in the container initially = 7x=(7×16×21)/(4×28)
=(16×21)/(4×4) =21