Average, Mixture and Alligation Question 7 - CAT 2022
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 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:
Step-by-Step Explanation
Let us assume both containers have a total capacity of 200 units. Since they are initially half-filled, we have:
- Container 1 = 100 units of pure sugar syrup (0 milk)
- Container 2 = 100 units of pure milk (0 sugar syrup)
Now track the three sequential liquid exchanges precisely:
- Transaction 1 (Half of Container 1 to Container 2):
50 units of sugar syrup move from Container 1 to Container 2.
Container 1 now holds: 50 units sugar syrup.
Container 2 now holds: 100 units milk + 50 units sugar syrup (Total = 150 units, Ratio = 2 : 1 milk to syrup).
- Transaction 2 (Half of Container 2 back to Container 1):
Half of Container 2's mixed volume (75 units) is sent back. This 75 units carries the internal 2 : 1 ratio, meaning it contains 50 units of milk and 25 units of sugar syrup.
Container 2 retains: 50 units milk + 25 units sugar syrup.
Container 1 now holds: 50 + 25 = 75 units sugar syrup + 50 units milk (Total = 125 units, Ratio = 3 : 2 syrup to milk).
- Transaction 3 (Half of Container 1 back to Container 2):
Half of Container 1's volume (62.5 units) is transferred to Container 2. This 62.5 units carries the internal 3 : 2 ratio, meaning it contains:
Syrup added = 3 / 5 × 62.5 = 37.5 units
Milk added = 2 / 5 × 62.5 = 25 units
- Final Composition of Container 2:
Final Sugar Syrup = 25 (retained) + 37.5 (added) = 62.5 units
Final Milk = 50 (retained) + 25 (added) = 75 units
Final Ratio (Syrup : Milk) = 62.5 : 75 = 5 : 6
Correct Option: D
💡 FundaMakers Tip:
For multi-stage back-and-forth liquid transfers, construct a simple running ledger matrix. Using a highly composite base volume like 200 ensures that the successive halving steps yield clean, manageable numbers, keeping your final ratio calculation straightforward.