Discussion
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?
Answer: C
Let the can hold \( 12k \) litres, with A \( = 7k \).
Drawing off 9 litres removes A in proportion, and adding B keeps the total at \( 12k \):
\[ \text{A left} = 7k - 9 \times \frac{7}{12} = 7k - 5.25 \]
The new ratio 7 : 9 makes A \( \tfrac{7}{16} \) of the total:
\[ \frac{7k - 5.25}{12k} = \frac{7}{16} \quad\Longrightarrow\quad 112k - 84 = 84k \]
\[ 28k = 84 \quad\Longrightarrow\quad k = 3 \]
\[ \text{A initially} = 7 \times 3 = 21 \text{ litres} \]
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