Explanation:

Let's analyze the problem to find out how many litres of liquid X was initially in the beaker:

- The initial ratio of X to Y is 5:3. Let's say the initial quantities of X and Y are 5k and 3k litres, respectively.

- A total of 6 litres of the mixture is drawn off, which will contain 6 * (5/8) = 3.75 litres of X and 6 * (3/8) = 2.25 litres of Y since they are in the ratio 5:3.

- The new quantity of X is 5k - 3.75.

- The new quantity of Y becomes 3k - 2.25 + 6 after adding 6 litres of Y.

- The new ratio is given as 5:7, leading to the equation (5k - 3.75) / (3k + 3.75) = 5 / 7.

Solving this equation for k gives us 2.25.

- To find the initial quantity of X: 5k = 5 * 2.25 = 11.25 litres.

- Correct answer is: Option 3: 11.25 litres

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