A milk man sells the milk at the cost price but he mixes the water in it and thus he gains 9.09%. The quantity of water in the mixture of 1 liter is :

Given:

• Gain = 9.09%
• Milk is sold at cost price
• Water is added → no cost → full gain comes from the water

Key Concept: When milk is sold at cost price and gain is made, the gain % is due to the addition of water. Therefore:

Gain% = (Water / Milk) × 100

So, using the gain:

9.09 = (Water / (1 - Water)) × 100

⇒ 9.09 / 100 = Water / (1 - Water)

Cross multiplying:

9.09(1 - W) = 100W
=> 9.09 - 9.09W = 100W
=> 9.09 = 109.09W
=> W = 9.09 / 109.09 ≈ 0.0833 liters

Convert to milliliters:

0.0833 liters = 83.33 ml

Answer: 83.33 ml of water is in 1 liter of the mixture.