To solve this problem, we need to understand the working principle of step-up and step-down transformers and the relationships between the voltages and the number of turns of the windings. The key formula we use is the transformer equation:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

where:

• $$V_p$$ is the primary voltage
• $$V_s$$ is the secondary voltage
• $$N_p$$ is the number of turns in the primary winding
• $$N_s$$ is the number of turns in the secondary winding

Let's break down the problem:

1. The power plant produces an electric power of 600 kW at 4000 V. 2. A step-up transformer is used at the plant side with a turns ratio of 1 : 10, i.e., $$N_p : N_s = 1 : 10$$.

This tells us that:

$$\frac{V_p}{V_s} = \frac{1}{10}$$

Since the primary voltage $$V_p$$ is 4000 V, we can find the secondary voltage $$V_s$$ as follows:

$$V_s = 10 \times V_p$$

$$V_s = 10 \times 4000$$

$$V_s = 40000$$ V

So, at the output of the step-up transformer, the voltage is 40000 V. This high voltage is then transported over the cables to the consumers' location 20 km away. At the consumers' end, a step-down transformer is used to reduce the voltage to 200 V to supply power to the consumers.

Now, we are given that the power supplied at the consumers' end must be 200 V. We need to find the ratio of the number of turns in the primary to the number of turns in the secondary for the step-down transformer so that it outputs 200 V from an input of 40000 V.

Using the transformer equation again, we can write:

$$\frac{V_p}{V_s} = \frac{N_p}{N_s}$$

where $$V_p = 40000$$ V and $$V_s = 200$$ V. Plugging these values in, we get:

$$\frac{40000}{200} = \frac{N_p}{N_s}$$

This simplifies to:

$$\frac{40000}{200} = 200$$

So, the turns ratio $$\frac{N_p}{N_s} = 200 : 1$$.

Thus, the correct answer is:

Option A: 200 : 1