Average, Mixture and Alligation Question 2 - CAT 2021
From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is:
Step-by-Step Explanation
- Analyze the Final State Ratio:
The final ratio of milk to water is 16 : 9. Out of a total mixture volume of 25 units, milk makes up exactly 16 / 25 of the container.
- Apply the Successive Dilution Formula:
Let the total container capacity be C. Since 9 litres are removed and replaced with water twice, the remaining fraction of milk is:
(1 − 9 / C)² = 16 / 25
- Solve for Capacity (C):
Take the square root of both sides:
1 − 9 / C = 4 / 5
9 / C = 1 / 5
C = 45 litres
The capacity of the container is 45 litres.
Correct Answer: 45
💡 FundaMakers Tip:
For all successive replacement workflows, the final quantity of the remaining core component follows the standard exponential format: Remaining/Total= (1 − Out/ Total)ⁿ. Recognizing the perfect squares 16 and 25 skips the need for expanding quadratic roots and isolates the variable directly.