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
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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