Question

A clock strikes once at 1 o'clock, twice at 2 o'clock and so on. If it takes 6 seconds to strike at 3 o'clock, how much time will it take to strike at 9 o'clock?

• A. 24 seconds
• B. 18 seconds
• C. 20 seconds
• D. None of these

Hint:

Count the gaps between strikes, not the strikes themselves; 3 strikes have only 2 gaps.

Answer 1

The Correct Option is A

This can also be solved using a direct ratio of intervals instead of first calculating the time for a single interval.

1. The key idea is that the time taken to strike a certain number of times depends on the number of gaps, or intervals, between the strikes, not on the number of strikes itself, since the interval is where the time is actually spent.
2. At 3 o'clock, the clock strikes 3 times, creating 3 - 1 = 2 intervals, and this takes 6 seconds.
3. At 9 o'clock, the clock strikes 9 times, creating 9 - 1 = 8 intervals.
4. Since the time is directly proportional to the number of intervals, set up a ratio: time for 9 o'clock divided by time for 3 o'clock equals intervals for 9 o'clock divided by intervals for 3 o'clock.
5. This gives: time for 9 o'clock / 6 = 8 / 2.
6. Solving, time for 9 o'clock = 6 x (8/2) = 6 x 4 = 24 seconds.

So it takes 24 seconds for the clock to strike at 9 o'clock, confirming option (1) as the correct answer. Simply scaling 6 seconds by the ratio of strikes, 3 to 9, would incorrectly give 18 seconds, since that ignores that the number of gaps, not the number of strikes, determines the time taken.