A certain amount of mixture contains milk and water in the ratio of 4 : 1.If 10 liters of this mixture is replaced by 10 liters of water, t…

Let the volume of water be = x

Then, volume of milk = 4x

Volume of Mixture replaced = 10 liters

Volume of water added = 10 liters

Volume of milk replaced = (4/5) × 10 = 8 liters

Volume of water replaced = 10 – 8 = 2 liters

Ratio of milk to water when mixture is replaced by 10 liters of water = 2 : 3

Initial, volume of milk = $(\frac{{4{\rm{x}} - 8}}{{{\rm{x}} - 2 + 10}} = \frac{2}{3})$

⇒ 12x – 24 = 2x + 16

⇒ 10x = 24 + 16

⇒ x = 40/10 = 4

∴ Volume of milk initially = 4 × 4 = 16 liters

∴ The initial volume of milk is 16 liters