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, then the resultant ratio becomes 2 : 3.How much pure milk was originally there in the mixture at first.
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, then the resultant ratio becomes 2 : 3.How much pure milk was originally there in the mixture at first.
1). 8 liters
2). 10 liters
3). 12 liters
4). 16 liters
1 answers
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
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