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: Build a general formula instead of solving one case at a time.
If a clock takes $T$ seconds to strike $n$ gongs, the time per gap is $\frac{T}{n-1}$, since $n$ gongs create only $n-1$ waiting gaps.

Step 2: Plug in the seven o'clock case to find the gap time.
Here $n=7$ and $T=7$, so gap time = $\frac{7}{7-1} = \frac{7}{6}$ seconds. This gap time is a fixed property of the clock, it stays the same no matter what hour it strikes.

Step 3: Use the formula again for eleven o'clock.
For eleven o'clock, $n=11$, so the number of gaps is $11-1=10$. Total time = $10 \times \frac{7}{6} = \frac{70}{6}$ seconds.

Step 4: Convert to decimal.
$\frac{70}{6} = 11.6666...$ seconds, which rounds to 11.66666667 seconds as given in the options.

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