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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 liters2). 10 liters3). 12 liters 4). 16 liters |
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Answer» 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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