Average, Mixture and Alligation Question 3 - CAT 2022
A glass contains 500 cc of milk and a cup contains 500 cc of water. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio:
Step-by-Step Explanation
Let us track the liquid volumes macroscopically:
- Initial state: Glass has 500 cc pure milk; Cup has 500 cc pure water.
When 150 cc of milk is added to the cup, the cup contains 650 cc of a mixture.
When 150 cc of this thoroughly blended mixture is moved back to the glass, the total volume of liquid in both containers returns to exactly 500 cc each.
Because the total liquid volume inside each container is restored to its original starting volume, any volume of milk missing from the glass must have been exactly replaced by an identical volume of water from the cup. Consequently, the volume of water now residing in the glass is exactly equal to the volume of milk left behind in the cup, yielding a perfect ratio of 1 : 1.
Correct Option: A
💡 FundaMakers Tip:
This is a famous conceptual shortcut! In any closed system where equal volumes of two distinct liquids are interchanged such that the final container volumes return to their initial state, the absolute quantity of impurity in container A will always be equal to the absolute quantity of impurity in container B. You don't need to do any calculation; the answer is dynamically constrained to be 1 : 1.