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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?

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? Correct Answer 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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