Question : Two vessels of equal capacity, and both completely filled, contain mixtures of milk and water in the ratio of 5 : 1 and 6 : 5, respectively. Both the mixtures are now mixed thoroughly. What is the ratio of milk to water in the new mixture so obtained?
Option 1: 105 : 67
Option 2: 57 : 41
Option 3: 91 : 41
Option 4: 28 : 43
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Correct Answer: 91 : 41
Solution : Given: Ratio of milk and water in 1st vessel = 5 :1 The ratio of milk and water in 2nd vessel = 6 : 5 Let both the vessels have $x$ litres of mixtures. Total quantity of milk = $\frac{5x}{6}+ \frac{6x}{11}=\frac{91x}{66}$ Total quantity of water = $\frac{x}{6}+\frac{5x}{11}=\frac{41x}{66}$ Required ratio = $\frac{91x}{66}:\frac{41x}{66}= 91 : 41$ Hence, the correct answer is 91 : 41.
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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
Question : The ratio of spirit and water in two mixtures of 46 litres and 50 litres is 11 : 12 and 2 : 3 respectively. Both the mixtures are mixed. Find the ratio of the spirit and water in the new mixture.
Option 1: 8 : 9
Option 2: 7 : 9
Option 4: 3 : 7
Question : Two beakers contain acid and water in the ratio 2 : 3 and 3 : 4 respectively. If equal volumes of the mixtures from these two beakers are poured into a common beaker, find the resultant ratio of acid to water in the mixture in the common beaker.
Option 2: 21 : 29
Option 3: 5 : 7
Option 4: 29 : 41
Question : A mixture of milk and water in three bottles of equal capacity is in the ratio 4 : 1, 4 : 3, and 1 : 2, respectively. 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: 179 : 136
Option 2: 152 : 165
Option 3: 198 : 175
Option 4: 133 : 145
Question : A mixture contains milk and water in a ratio of 9 : 5. When 6 litres of water is added to this mixture, the ratio of milk and water becomes 9 : 7. Find the quantity of milk in the mixture.
Option 1: 30 litres
Option 2: 18 litres
Option 3: 27 litres
Option 4: 15 litres
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