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4 L is Drawn from a Container Full of Milk and Then is Filled with Water. this Operation is Performed Three More Times. the Ratio of the Quantity of Milk Left in the Container and that of Water is 16 - Mathematics

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MCQ

4 L is drawn from a container full of milk and then is filled with water. This operation is performed three more times. The ratio of the quantity of milk left in the container and that of water is 16 : 65. How much milk did the container hold initially?

Options

  • 24L

  • 12L

  • 15L

  • 25 L

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Solution

12 L

Explanation:
According to the formula,
After n operations, the quantity of pure liquid

= `["a"(1 - "b"/"a")^"n"]` units

Here, b = 4, n = 4, a = ?
Quantity of milk left in the container after four operations = `["a"(1 - 4/"a")^"n"]`L

Then, according to the question,

`"Quantity of milk left"/"Quantity of water" = 16/81`

⇒ `(a[(1-4/a)^4])/a=16/(65+16)=16/81`

⇒ `(1-4/a)^4=16/81`

⇒ `1-4/a=2/3`

⇒ `4/a=1/3`

∴ a = 12L

Concept: Ratio and Proportion (Entrance Exam)
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