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1. A bucket contains a mixture of two liquids A and B in the proportion 7 : 5. If 9 litres of mixture is replaced by 9 liters of liquid B, then the ratio of the two liquids becomes 7 : 9. How much of the liquid A was there in the bucket ?

A. 21 liters

B. 23 liters

C. 25 liters

D. 27 liters

Solution:

Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively.When 9 litres of mixture are drawn off, quantity of A in mixture left:

\begin{aligned} = [7 x - \frac{7}{12} \times 9] litres \\ = [7 x - \frac{21}{4}] litres \\ Similarly quantity of B in mixture left, \\ = [5 x - \frac{5}{12} \times 9] litres \\ = [5 x - \frac{15}{4}] litres \\ ∴ ratio becomes, \\ \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 \\ So the can contained, \\ = 7 \times x \\ = 7 \times 3 \\ = 21 litres of A initially . \end{aligned}

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