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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)
    4 : 5
  • b)
    6 : 5
  • c)
    5 : 4
  • d)
    5 : 6
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
There are two containers of the same volume, first container half-fill...
Given:
- Two containers of the same volume.
- First container is half-filled with sugar syrup.
- Second container is half-filled with milk.

Process:
1. Half the content of the first container is transferred to the second container.
2. Half of this mixture is transferred back to the first container.
3. Half the content of the first container is transferred back to the second container.

To find:
The ratio of sugar syrup and milk in the second container.

Solution:
Let's assume that the volume of each container is 'V'. Initially, the first container is half-filled, so it contains V/2 sugar syrup, and the second container is half-filled with V/2 milk.

Step 1: Half the content of the first container is transferred to the second container.
- The first container now contains V/4 sugar syrup (half of V/2).
- The second container now contains V/4 sugar syrup (half of V/2) and V/2 milk (unchanged).

Step 2: Half of this mixture is transferred back to the first container.
- The first container now contains V/8 sugar syrup (half of V/4) and V/8 milk (half of V/4).
- The second container now contains V/8 sugar syrup (half of V/4) and V/4 milk (unchanged).

Step 3: Half the content of the first container is transferred back to the second container.
- The first container now contains V/16 sugar syrup (half of V/8) and V/16 milk (half of V/8).
- The second container now contains V/16 sugar syrup (half of V/8) and V/8 milk (unchanged).

Final Ratio:
The ratio of sugar syrup to milk in the second container is V/16 : V/8, which simplifies to 1 : 2.

Answer:
The ratio of sugar syrup to milk in the second container is 1 : 2, which is equivalent to 5 : 10 or 5 : 6. Therefore, the correct answer is option D) 5 : 6.
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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 isa)4 : 5b)6 : 5c)5 : 4d)5 : 6Correct answer is option 'D'. Can you explain this answer?
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