This problem can be solved using the concept of successive reduction.

Step 1: Understand the problem
The problem states that 8 liters of wine are drawn from a cask and replaced with water. This operation is performed 4 times in total. After these operations, the ratio of wine to water is 16:65. We need to find the original quantity of wine in the cask.

Step 2: Formulate the equation
Let's denote the original quantity of wine as 'x'. After each operation, the quantity of wine is reduced by 8 liters and replaced with water. However, since the operation is performed on the mixture (wine + water), the quantity of wine is reduced by a fraction each time. This fraction is (x-8)/x. Since the operation is performed 4 times, the fraction is raised to the power of 4.

So, the equation becomes:
(x-8)^4/x^4 = 16/65

Step 3: Solve the equation
To simplify the equation, we can take the fourth root on both sides:
(x-8)/x = (fourth root of 16/65)

Solving this equation gives us x ≈ 32 liters.

So, the cask originally held approximately 32 liters of wine. Therefore, the correct answer is 32 Litres.

Question

This problem can be solved using the concept of successive reduction.

Step 1: Understand the problem
The problem states that 8 liters of wine are drawn from a cask and replaced with water. This operation is performed 4 times in total. After these operations, the ratio of wine to water is 16:65. We need to find the original quantity of wine in the cask.

Step 2: Formulate the equation
Let's denote the original quantity of wine as 'x'. After each operation, the quantity of wine is reduced by 8 liters and replaced with water. However, since the operation is performed on the mixture (wine + water), the quantity of wine is reduced by a fraction each time. This fraction is (x-8)/x. Since the operation is performed 4 times, the fraction is raised to the power of 4.

So, the equation becomes: 
(x-8)^4/x^4 = 16/65

Step 3: Solve the equation
To simplify the equation, we can take the fourth root on both sides:
(x-8)/x = (fourth root of 16/65)

Solving this equation gives us x ≈ 32 liters.

So, the cask originally held approximately 32 liters of wine. Therefore, the correct answer is 32 Litres.

Knowee AI · Accepted Answer

This problem can be solved using the concept of successive reduction.

Step 1: Understand the problem
The problem states that 8 liters of wine are drawn from a cask and replaced with water. This operation is performed 4 times in total. After these operations, the ratio of wine to water is 16:65. We need to find the original quantity of wine in the cask.

Step 2: Formulate the equation
Let's denote the original quantity of wine as 'x'. After each operation, the quantity of wine is reduced by 8 liters and replaced with water. However, since the operation is performed on the mixture (wine + water), the quantity of wine is reduced by a fraction each time. This fraction is (x-8)/x. Since the operation is performed 4 times, the fraction is raised to the power of 4.

So, the equation becomes: 
(x-8)^4/x^4 = 16/65

Step 3: Solve the equation
To simplify the equation, we can take the fourth root on both sides:
(x-8)/x = (fourth root of 16/65)

Solving this equation gives us x ≈ 32 liters.

So, the cask originally held approximately 32 liters of wine. Therefore, the correct answer is 32 Litres.

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