Question : Three bottles of equal capacity contain mixtures of milk and water in ratios 2 : 5, 3 : 4, and 4 : 5. These three bottles are emptied into a large bottle. What will be the ratio of milk and water respectively in the large bottle?
Option 1: 73 : 106
Option 2: 73 : 116
Option 3: 73 : 113
Option 4: 73 : 189
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Correct Answer: 73 : 116
Solution :
Let the capacity of each bottle be $x$ units.
Bottle 1 has milk : water = 2 : 5
Bottle 2 has milk : water = 3 : 4
Bottle 3 has milk : water = 4 : 5
Bottle 1 contains milk = $\frac{2x}{7}$, water = $\frac{5x}{7}$
Bottle 2 contains milk = $\frac{3x}{7}$, water = $\frac{4x}{7}$
Bottle 3 contains milk = $\frac{4x}{9}$, water = $\frac{5x}{9}$
When mixed, the ratio of milk and water is:
$= (\frac{2x}{7}+\frac{3x}{7}+\frac{4x}{9}) : (\frac{5x}{7}+\frac{4x}{7}+\frac{5x}{9})$
$= (\frac{18x+27x+28x}{63}) : (\frac{45x+36x+35x}{63})$
$= 73: 116$
Hence, the correct answer is 73 : 116.
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