Question

A jar has 40 L milk. From the jar, 8 L of milk was taken out and replaced by an equal quantity of water. If 8 L of the newly formed mixture is taken out of the jar, what is the final quantity of milk left in the jar?

• A. 32.5L
• B. 30L
• C. 25.6L
• D. 24.2L

Answer 1

Answer:

C. 25.6L

Step-by-Step Calculation

1. Initial State:

   • The jar initially contains 40 L of pure milk.

   • There is 0 L of water.

   • The total volume in the jar is 40 L.

2. First Operation: 8 L of milk is taken out and replaced by 8 L of water.

   • Milk remaining after removal: 40 L - 8 L = 32 L.

   • Water added: 8 L.

   • Total volume after replacement: 32 L (milk) + 8 L (water) = 40 L. The total volume remains constant after replacement.

   • Concentration of milk (or fraction of milk) in the mixture: 32 L (milk) / 40 L (total volume) = 4/5.

3. Second Operation: 8 L of the newly formed mixture is taken out.

   • When 8 L of the mixture is removed, both milk and water are removed proportionally to their concentration in the mixture.

   • The current concentration (or fraction) of milk in the mixture is 4/5.

   • Quantity of milk removed in this step: 8 L (mixture removed) * (4/5) (fraction of milk) = 32/5 L = 6.4 L.

   • Final quantity of milk left in the jar: Milk present before this step - Milk removed in this step = 32 L - 6.4 L = 25.6 L.