Question

Mohan has an antique clock which strikes and makes a loud gong sound every hour. It strikes the exact number of times indicating the time of the day or night. His clock takes seven seconds to strike Seven O'clock. How many seconds will his clock take to strike Eleven O'clock?

• A. 11.22222227 seconds
• B. 11 seconds
• C. 11.66666667 seconds
• D. None of the above

Hint:

A clock striking n times has only n minus 1 gaps between the gongs, not n gaps, so find the time per gap first.

Answer 1

The Correct Option is C

Step 1: Count gaps, not gongs.
Striking seven o'clock means 7 gongs sound, but the clock only needs to wait through the gaps between them. With 7 gongs there are only 6 gaps, because the very first gong needs no waiting time at all.

Step 2: Find the length of one gap.
6 gaps take a total of 7 seconds, so one gap takes \( \frac{7}{6} \) seconds.

Step 3: Apply this to eleven o'clock.
Striking eleven o'clock means 11 gongs, so there are 11 minus 1 = 10 gaps between them.

Step 4: Multiply gap length by number of gaps.
Total time = \( 10 \times \frac{7}{6} = \frac{70}{6} \) seconds, which works out to about 11.67 seconds.

Final Answer:
The clock takes about 11.66666667 seconds to strike eleven o'clock. \[ \boxed{\frac{70}{6} \approx 11.67 \text{ seconds}} \]