Question : Two vessels A and B contain milk and water mixed in the ratios 4 : 3 and 2 : 3. The ratio in which these mixtures need to be mixed to form a new mixture containing half milk and half water is:
Option 1: 7 : 5
Option 2: 6 : 5
Option 3: 5 : 6
Option 4: 4 : 3
Correct Answer: 7 : 5
Solution :
Given:
In vessel A, the ratio of milk and water = 4 : 3
In vessel B, the ratio of milk and water = 2 : 3
According to the question,
Let the two mixtures be mixed in the ratio $x:y$
In $x$ litre of mixture A, the volume of milk = $\frac{4x}{7}$
In $x$ litre of mixture A, the volume of water = $\frac{3x}{7}$
In $y$ litre of mixture B, the volume of milk = $\frac{2y}{5}$
In $y$ litre of mixture B, the volume of water = $\frac{3y}{5}$
According to the question,
$\frac{4x}{7}$ + $\frac{2y}{5}$ = $\frac{3x}{7}$ + $\frac{3y}{5}$
or, $\frac{20x + 14y}{35}$ = $\frac{15x + 21y}{35}$
or, 20$x$ + 14$y$ = 15$x$ + 21$y$
or, 5$x$ = 7$y$
or, $\frac{x}{y}$ = $\frac{7}{5}$
Hence, the correct answer is 7 : 5.
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