Question
A container has 60 litres of a mixture of milk and water in the ratio 7 : 3. Some quantity of water is added to this mixture so that the new ratio of milk to water becomes 3 : 2. How many litres of water were added?
Solution
ATQ, Initial mixture = 60 L Milk : Water = 7 : 3 Amount of milk = (7/10) × 60 = 42 L Amount of water = (3/10) × 60 = 18 L Let x litres of water be added. New milk = 42 L (unchanged) New water = 18 + x New ratio milk : water = 3 : 2 So, 42 : (18 + x) = 3 : 2 ⇒ 42 / (18 + x) = 3 / 2 Cross-multiply: 2 × 42 = 3(18 + x) 84 = 54 + 3x 3x = 30 x = 10 So, water added = 10 litres.
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