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
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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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