Question

A bottle contains 50 liters of milk. From this bottle 5 liters of milk was taken out and replaced the water. This process was repeated further for three times. How much milk is now contained in the bottle ?

• A. 32.8 litres
• B. 34.4 litres
• C. 36.8 litres
• D. 46.5 litres

Answer 1

The Correct Option is A

To solve this problem, we can use the concept of successive dilution. When 5 liters of milk is removed from the 50-liter mixture and replaced with water, the proportion of milk left in the mixture is reduced each time this process is repeated. Let's step through the calculations:

• Initially, the bottle contains 50 liters of milk.
• After the first extraction, 5 liters are taken out, which is 10% of 50 liters. Therefore, 90% of milk remains.
  Remaining milk after 1st extraction = 50 × 0.9 = 45 liters.
• Repeat the process for the second time; again, 10% of 45 liters is removed, so 90% of 45 liters remains.
  Remaining milk after 2nd extraction = 45 × 0.9 = 40.5 liters.
• For the third extraction, 10% of 40.5 liters is taken out, so 90% remains.
  Remaining milk after 3rd extraction = 40.5 × 0.9 = 36.45 liters.
• Finally, for the fourth extraction, 10% of 36.45 liters is taken out, leaving 90% remaining.
  Remaining milk after 4th extraction = 36.45 × 0.9 = 32.805 liters.

Rounding 32.805 liters, we find the amount of milk left in the bottle is 32.8 liters.

Step	Remaining Milk (Liters)
Initial	50.0
After 1st Extraction	45.0
After 2nd Extraction	40.5
After 3rd Extraction	36.45
After 4th Extraction	32.8

Therefore, the correct answer is 32.8 liters.