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In a mixture of ghee and dalda, the ratio of ghee to dalda is 5 : a. When 5 litres of ghee were added in the mixture then, the concentration of dalda becomes 50% but when 2 litres of dalda were added in the mixture then the concentration of ghee becomes 40%. Quantity I : ghee will be what part of the mixture when, 10 litres of ghee were added in the original mixture?Quantity II : Dalda will be what part of the mixture when 3 litres of dalda were added in the original mixture?1. Quantity 1 > Quantity 22. Quantity 1 ≥ Quantity 23. Quantity 1 < Quantity 24. Quantity 1 ≤ Quantity 25. Quantity 1 = Quantity 2 |
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Answer» Correct Answer - Option 3 : Quantity 1 < Quantity 2 Given: Ghee : Dalda = 5 : a Calculation: Let the quantity of ghee = 5x litres ⇒ the quantity of Dalda = ax litres According to the question, ax = 50% of (5x + ax + 5) ⇒ 2ax = 5x + ax + 5 ⇒ ax = 5x + 5 ….(i) ⇒ 5x = 40% of (5x + ax + 2) ⇒ 25x = 10x + 2ax + 4 ⇒ ax = (15x – 4)/2 ….(ii) From the equation (i) and (ii) ⇒ 5x + 5 = (15x – 4)/2 ⇒ 5x = 14 ⇒ x = 14/5 Put the value of x in the equation (i) ⇒ a = 95/14 The quantity of ghee in the original mixture = 5x = 14 litres ⇒ the quantity of dalda = ax ⇒ quantity of dalda = 19 litres Quantity I : when, 10 litres of ghee were added in the original mixture ghee = (14 + 10) / (14 + 19 + 10) ⇒ ghee = 24/43 Quantity II: when 3 litres of dalda were added in the original mixture ⇒ dalda = (19 + 3) / (14 + 19 + 3) ⇒ dalda = 11/18 ∴ Quantity I < Quantity II |
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