Question

In a watch, the minute hand crosses the hour hand for the third time exactly after every 3 hours 18 minutes and 15 seconds of watch time. What is the time gained or lost by this watch in one day?

• A. 14 min 10 s lost
• B. 13 min 50 s lost
• C. 13 min 20 s gained
• D. 14 min 40 s gained

Hint:

To calculate time gained or lost, compare the given time for a cycle with the actual time, then convert the difference into minutes and seconds.

Answer 1

The Correct Option is D

The minute hand crosses the hour hand every 3 hours 18 minutes and 15 seconds in the watch time. Step 1: Convert the time of crossing to seconds: \[ 3 \, \text{hr} = 3 \times 60 \times 60 = 10,800 \, \text{seconds}, \quad 18 \, \text{min} = 18 \times 60 = 1,080 \, \text{seconds}, \quad 15 \, \text{seconds} \] So, the total time for each crossing is: \[ 10,800 + 1,080 + 15 = 11,895 \, \text{seconds}. \] Step 2: The minute hand crosses the hour hand every \(11,895\) seconds of the watch time, but the actual time taken is \(3600\) seconds (1 hour). Step 3: Find the difference between the actual time and the watch time: \[ 11,895 - 3600 = 14,40 \, \text{seconds}. \] Step 4: Convert \(14,40\) seconds into minutes: \[ 14,40 \, \text{seconds} = 14 \, \text{minutes} \, 40 \, \text{seconds}. \] Thus, the time gained by the watch is: 14 min 40 s gained.