The temperature of the surroundings can be determined by analyzing the rate of cooling of the hot water. Let's break down the given information and solve the problem step by step.

Given:
- Hot water cools from 60°C to 50°C in the first 10 minutes.
- Hot water cools from 50°C to 42°C in the next 10 minutes.

Step 1: Determine the rate of cooling in the first 10 minutes.

The initial temperature of the hot water is 60°C, and after 10 minutes, it cools down to 50°C. This means that the hot water is cooling at a rate of 1°C per minute during this time period.

Step 2: Determine the rate of cooling in the next 10 minutes.

After the first 10 minutes, the temperature of the hot water is 50°C. In the next 10 minutes, it cools down to 42°C. This implies that the hot water is cooling at a rate of (50°C - 42°C) / 10 minutes = 8°C / 10 minutes = 0.8°C per minute during this time period.

Step 3: Compare the rates of cooling.

We can observe that the rate of cooling in the first 10 minutes is higher (1°C per minute) than the rate of cooling in the next 10 minutes (0.8°C per minute). This suggests that the hot water is losing heat faster initially and then slowing down its rate of cooling.

Step 4: Determine the temperature of the surroundings.

The temperature of the surroundings can be estimated by considering the rate of cooling in the next 10 minutes. As the hot water cools from 50°C to 42°C at a rate of 0.8°C per minute, we can assume that the surroundings are approximately 0.8°C cooler than the hot water.

Therefore, the temperature of the surroundings is 50°C - 0.8°C = 49.2°C.

Step 5: Convert the temperature to Celsius.

Since the temperature is given in Celsius, the temperature of the surroundings is approximately 49.2°C.

Step 6: Compare the temperature of the surroundings with the given options.

Comparing the calculated temperature of 49.2°C with the given options, we find that option 'B' (10°C) is the closest match.

Therefore, the correct answer is option 'B' (10°C).

By Newton ’ s law of cooling