Discussion
A milkman had water and milk mixture in a can with water to milk ratio 5:7. He accidently spills 9 liters of the mixture. He then fills the can with water equal in quantity to spilled mixture. This makes the water to milk ratio 9:7. How much milk did the can initially have?
Answer: A
Let the can hold \( T \) litres, with milk \( \tfrac{7T}{12} \).
Spilling 9 litres removes milk in proportion, and the water added keeps the total at \( T \):
\[ \text{milk left} = \frac{7T}{12} \cdot \frac{T-9}{T} = \frac{7(T-9)}{12} \]
The new ratio 9 : 7 makes milk \( \tfrac{7T}{16} \):
\[ \frac{7(T-9)}{12} = \frac{7T}{16} \quad\Longrightarrow\quad 16(T-9) = 12T \]
\[ 4T = 144 \quad\Longrightarrow\quad T = 36 \]
\[ \text{milk} = \frac{7 \times 36}{12} = 21 \text{ litres} \]
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