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1. 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?

A. 10

B. 20

C. 21

D. 25

Solution:

\begin{aligned} Suppose the can initially contains \\ 7 x and 5 x of mixtures A and B respectively . \\ Quantity of A in mixture left \\ = (7 x - \frac{7}{12} \times 9) litres \\ = (7 x - \frac{21}{4}) litres \\ Quantity of B in mixture left \\ = (5 x - \frac{5}{12} \times 9) litres \\ = (5 x - \frac{15}{4}) litres \\ ∴ \frac{(7 x - \frac{21}{4})}{(5 x - \frac{15}{4}) + 9} = \frac{7}{9} \\ \Rightarrow \frac{28 x - 21}{20 x + 21} = \frac{7}{9} \\ \Rightarrow 252 x - 189 = 140 x + 147 \\ \Rightarrow 112 x = 336 \\ \Rightarrow x = 3 \end{aligned}

So, the can contained 21 litres of A

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