A certain pressure 'P' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is $$\frac{3}{x}$$. The value of $$x$$ is _____.

We have the same pressure $$P$$ applied to 1 litre of water and 2 litres of a liquid. Water gets compressed by 0.01% and the liquid by 0.03%.

The bulk modulus is defined as:

$$B = \frac{P}{\frac{\Delta V}{V}}$$

Note that the fractional compression $$\frac{\Delta V}{V}$$ is independent of the initial volume, so the volume of liquid (2 litres vs 1 litre) does not affect the bulk modulus calculation.

For water: $$B_w = \frac{P}{0.01\%} = \frac{P}{0.0001}$$

For the liquid: $$B_l = \frac{P}{0.03\%} = \frac{P}{0.0003}$$

Now the ratio of bulk moduli is:

$$\frac{B_w}{B_l} = \frac{P/0.0001}{P/0.0003} = \frac{0.0003}{0.0001} = 3 = \frac{3}{1}$$

We are given that the ratio is $$\frac{3}{x}$$, so:

$$\frac{3}{x} = 3 \implies x = 1$$

Hence, the answer is $$1$$.