In a mixture of 240 lt. water is 20% and rest is Milk. What quantity of mixture should be taken out and replaced with water so that water becomes 40%?

Step 1: Understand the initial setup

• Total mixture = 240 liters
• Water = 20% of 240 = 48 liters
• Milk = 240 - 48 = 192 liters

Let x liters of mixture be removed and replaced with water.

• In x liters of mixture, water is 20%, so water removed = 0.2x
• Milk removed = 0.8x
• When x liters are removed, 0.8x liters of milk is removed.
• We replace the x liters entirely with water.

New quantities after replacement:

• Water = Existing water (48 - 0.2x) + x (added water) = 48 - 0.2x + x = 48 + 0.8x
• Milk = 192 - 0.8x

We want water to become 40% of the new mixture (which is still 240 liters):

(48 + 0.8x) / 240 = 40/100
⇒ 48 + 0.8x = 96
⇒ 0.8x = 96 - 48 = 48
⇒ x = 48 / 0.8 = 60

Answer: 60 liters

We must take out 60 liters of the original mixture and replace it with water to make water 40% of the total mixture.

This problem is a practical example of the replacement technique, commonly seen in quantitative aptitude tests and exams. It demonstrates how the concentration of one component in a mixture can be adjusted through successive replacement — a concept applicable in industrial mixing, solutions preparation, and dilution problems.