Question

There are two containers of the same volume,first container half-filled with sugar syrup and the second container half-filled with milk.Half the content of the first container is transferred to the second container,and then the half of this mixture is transferred back to the first container.Next, half the content of the first container is transferred back to the second container.Then the ratio of sugar syrup and milk in the second container is

• A. \(5\ratio6\)
• B. \(5\ratio4\)
• C. \(6\ratio5\)
• D. \(4\ratio5\)

Answer 1

The Correct Option is A

The correct answer is A: \(5\ratio6\)
Given: 
-Two containers of the same volume. 
-First container is half-filled with sugar syrup,and the second container is half-filled with milk. 
Step 1: Transfer from First to Second Container
-Half the content of the first container is transferred to the second container. 
Now,the first container is left with \((\frac{1}{2}\times\frac{1}{2}=\frac{1}{4})\) of its initial content,which is sugar syrup. 
The second container has \(\frac{1}{2}+\frac{1}{4}=\frac{3}{4}\) of its volume filled with milk. 
Step 2: Transfer from Second to First Container
- Half of the mixture of the second container (which is \((\frac{3}{4} )\)) is transferred back to the first container. 
The first container now contains \(( \frac{1}{4} + \frac{3}{4} \times \frac{1}{2} = \frac{5}{8})\) of its volume filled with sugar syrup. 
The second container is left with \(( \frac{3}{4} \times \frac{1}{2} = \frac{3}{8})\) of its volume filled with milk. 
Step 3: Transfer from First to Second Container Again 
- Half the content of the first container (which is \(\frac{5}{8}\)) is transferred back to the second container. 
The second container now contains \(( \frac{3}{8} + \frac{5}{8} \times \frac{1}{2} = \frac{11}{16})\) of its volume filled with milk. 
Final Result:
-\(Sugar syrup\ratio{Milk\space{in}\space{second}\space{container}}=( 62.5\ratio{75}=5\ratio{6})\) 
Therefore, the correct ratio of sugar syrup to milk in the second container is indeed \(5\ratio6\).

Answer 2

Considering that each container has a 200 liter capacity. 
Thus, 100 liters of sugar syrup are in Container 1 and 100 liters of milk are in Container 2.

Following the initial transfer, 
50 L of sugar syrup are in Container 1, and 50 L of milk and sugar syrup are in Container 2. 

Following the second move, 
50 L of milk and 25 L of sugar, or half of the second container, will be moved to container 1. 

Thus, 50 L of milk and 75 L of sugar syrup are in Container 1, and 50 L of milk and 25 L of sugar syrup are in Container 2. 

Following the third transfer, 
25 L of milk and 37.5 L of sugar syrup from the first container are transferred to the second container. 

Thus, 75 L of milk and 62.5 L of sugar syrup are in the second container.
The ratio of Sugar Syrup to milk in the second container is 5 : 6.