Hello,
The given numerical is quite easy but tricky example of ratio and proportion.
Consider first vessel,
The ratio of water to alcohol is 1 : 2
Now, 6 L solution is taken from first vessel.
Let, quantity of water be x. So, quantity of alcohol will be 2x.
So, x + 2x = 6
So, x = 2 L and 2x = 4L
Hence, 2 Liters of water and 4 liters of alcohol is taken out from first vessel.
Similarly, now consider 2nd vessel.
The ratio of water to alcohol is 3:4
35 Liters of solution is taken out.
Let, quantity of water taken out = 3x
So, quantity of alcohol taken out = 4x
Now, 3x + 4x = 35
So, x= 5
Hence, quantity of water taken out = 3x = 15 Liters
and quantity of Alcohol taken out = 4x = 20 Liters
Now, Solution is made by mixing 6L of solution from first vessel and 35L of solution from second vessel.
So, Total quantity of water in resultant solution = 15 L + 2 L = 17 L
and Total quantity of alcohol in resultant solution = 20L + 4L = 24 L
Hence, Ratio of Alcohol to Water in resultant solution = 24 : 17
Best Wishes.
Question : The alcohol and water in a mixture are in the ratio of 4 : 5 respectively. 20-litres water is added to it. If the ratio of alcohol and water in the new mixture is 1 : 3 respectively, then what is the total quantity of the alcohol in the new mixture?
Option 1: $\frac{80}{7}$ liters
Option 2: $15$ liters
Option 3: $\frac{60}{7}$ liters
Option 4: $\frac{90}{11}$ liters
Question : Two vessels contain milk and water in the ratios 3 : 2 and 7 : 3. Find the ratio in which the contents of the two vessels have to be mixed to get a new mixture in which the ratio of milk and water is 2 : 1.
Option 1: 2 : 1
Option 2: 1 : 2
Option 3: 4 : 1
Option 4: 1 : 4
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 : Two vessels of equal capacity contain juice and water in the ratio of 3 : 5 and 3 : 1 respectively. The mixture of both vessels is mixed and transferred into a bigger vessel. What is the ratio of juice and water in the new mixture?
Option 1: 13 : 9
Option 2: 9 : 7
Option 3: 8 : 9
Option 4: 7 : 3
Question : A vessel initially contains 60 litres of milk. First, 12 litres of milk is taken out from the vessel and replaced with water. The process is repeated a second time by taking out the same amount of milk and replacing it with water. What is the final ratio of milk to water in the resultant mixture?
Option 1: 15 : 10
Option 2: 16 : 9
Option 3: 9 : 5
Option 4: 16 : 10
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