There are two clocks, both sets to show the correct time at 9:00 AM. One clock loses 1 minute every hour and the other gains 1 minute every hour. By how many minutes do they differ at 10:00 PM on the same day? Choose the correct option.

• (A). 24 minutes
• (B). 30 minutes
• (C). 28 minutes
• (D). 26 minutes
• (E). 13 minutes

To determine how much the two clocks differ by 10:00 PM, we first need to calculate how long they have been running since 9:00 AM. From 9:00 AM to 10:00 PM is 13 hours.

Clock Calculations

Clock Losing Time

The first clock loses 1 minute every hour. Over 13 hours, it will lose:

• 1 minute/hour × 13 hours = 13 minutes

At 10:00 PM, this clock will show:

• 9:00 AM - 13 minutes = 8:47 PM

Clock Gaining Time

The second clock gains 1 minute every hour. Over the same 13 hours, it will gain:

• 1 minute/hour × 13 hours = 13 minutes

At 10:00 PM, this clock will show:

• 9:00 AM + 13 minutes = 9:13 AM

Finding the Difference

Now, we can find the difference between the two clocks:

• 9:13 AM - 8:47 PM = 24 minutes

Thus, the two clocks differ by 24 minutes at 10:00 PM.

Final Answer

The correct option is (A) 24 minutes.