Explanation:

Let's break down the problem step by step to understand how to arrive at the correct answer.

Step 1: Understand the problem

The problem states that a lady looked at her watch between 5 and 6. However, she mistakenly thought that the hour hand was the minute hand, leading her to believe that the time was 57 minutes earlier than the correct time. We need to determine the correct time based on this information.

Step 2: Analyze the situation

Since the lady mistook the hour hand for the minute hand, we need to consider the position of the hour hand as the minute hand and vice versa. This means that the minute hand will be pointing at the hour, and the hour hand will be pointing at the minute.

Step 3: Determine the position of the hour hand

To find the position of the hour hand, we need to calculate the angle it makes with the 12 o'clock position. At 5 o'clock, the hour hand will be at the 5-hour mark, which is 1/12th of a full circle. We can calculate the angle as follows:

Angle made by hour hand = (1/12) * 360 degrees = 30 degrees

Step 4: Determine the position of the minute hand

Since the hour hand is mistaken as the minute hand, we need to determine the position of the minute hand in terms of minutes. At 5 o'clock, the minute hand will point at the 12, which represents 60 minutes.

Step 5: Calculate the difference between the positions

Since the lady mistook the hour hand for the minute hand, she believed that the time was 57 minutes earlier than the correct time. Therefore, we can calculate the difference between the positions of the hour and minute hands as follows:

Difference in positions = 60 minutes - 57 minutes = 3 minutes

Step 6: Calculate the correct time

To determine the correct time, we need to add the difference in positions to the mistaken time. The mistaken time is 5 o'clock, which means the minute hand points at the 5 on the clock. Adding the difference of 3 minutes, we get:

Correct time = 5:03

Step 7: Convert the correct time to minutes past 5

Since the correct time is 5:03, we need to determine the number of minutes past 5. Subtracting 5:00 from 5:03, we get:

Number of minutes past 5 = 3 minutes

Conclusion:

Therefore, the correct time is 3 minutes past 5, which is equivalent to option B: 24 minutes past 5.