Question
In a mixture of milk and water, the ratio of milk to
water is 5 : 3. How much water must be added to 24 litres of this mixture so that the ratio becomes 3 : 5?Solution
Total mixture = 24 litres Milk = (5 / 8) × 24 = 15 litres Water = (3 / 8) × 24 = 9 litres Let x litres of water be added. New amount of water = 9 + x Milk = 15 litres (unchanged) New ratio milk : water = 3 : 5 So, 15 : (9 + x) = 3 : 5 ⇒ 15 / (9 + x) = 3 / 5 ⇒ 15 × 5 = 3(9 + x) ⇒ 75 = 27 + 3x ⇒ 75 − 27 = 3x ⇒ 48 = 3x ⇒ x = 16 Answer: 16 litres of water must be added.
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