Question

A container has a mixture of milk and water in the ratio 5 : 2. If 14 liters of this mixture is removed and replaced with water, the ratio becomes 5 : 4. What is the initial quantity of the mixture?

• A. 63 L
• B. 35 L
• C. 49 L
• D. 56 L

Hint:

In mixture replacement problems, focus on the substance whose quantity is not directly being replenished. The final amount of that substance is equal to its initial amount in the reduced volume. For this problem: Final Milk = (Initial Milk Proportion) \(\times\) (Initial Volume - Volume Removed). This can often lead to a faster solution.

Answer 1

The Correct Option is A

Step 1: Let the total volume be \( T \). Initially milk \( =\frac{5}{7}T \).
Step 2: Removing 14 L of mixture removes milk in the same 5:2 ratio, taking away \( \frac{5}{7}\times14=10 \) L of milk. Remaining milk \( =\frac{5}{7}T-10 \) (adding water back doesn't change this milk amount).
Step 3: The new ratio 5:4 means milk is now \( \frac{5}{9} \) of the (unchanged) total \( T \). Equate the two expressions for remaining milk:
\[ \frac{5}{7}T-10 = \frac{5}{9}T. \]
Step 4: Solve:
\[ \left(\frac{5}{7}-\frac{5}{9}\right)T = 10 \implies \frac{10}{63}T = 10 \implies T = \boxed{63\text{ L}}. \]