At 6 o clock a clock strikes 6 times, and the time between the first and the last strike is 30 seconds. Assuming the interval between any two consecutive strikes is constant, how long (in seconds) will it take to strike 12 times at 12 o clock?

Introduction / Context:
This question is about the striking pattern of a clock rather than the rotation of its hands. Many aptitude exams include such problems where you are given the time between the first and last strike for a certain hour and asked to predict the time taken to strike a different number of times. The key idea is that the time refers to the intervals between strikes, not to the number of strikes themselves.

Given Data / Assumptions:

• At 6 o clock, the clock strikes 6 times.
• The time between the first strike and the last strike at 6 o clock is 30 seconds.
• The interval between any two consecutive strikes is constant.
• We must find the time between the first and last strike when the clock strikes 12 times at 12 o clock.

Concept / Approach:
If a clock strikes n times, then there are not n intervals but rather n minus 1 equal intervals between the first and last strike. The given time refers to the sum of these intervals. Once we know the length of one interval, we can easily compute the time required for any other number of strikes by multiplying the interval by the number of gaps, that is, the new number of strikes minus one.

Step-by-Step Solution:
Step 1: At 6 o clock the clock strikes 6 times, creating 6 - 1 = 5 equal intervals between the first and last strike. Step 2: The total time for these 5 intervals is given as 30 seconds. Step 3: Therefore, the time per interval is: interval time = 30 / 5 = 6 seconds. Step 4: At 12 o clock, the clock must strike 12 times. Step 5: The number of intervals between the first and last strike at 12 o clock is 12 - 1 = 11 intervals. Step 6: Each interval is 6 seconds, so the total time for all 11 intervals is: total time = 11 * 6 = 66 seconds. Step 7: Thus, it will take 66 seconds for the clock to complete 12 strikes at 12 o clock.

Verification / Alternative check:
An easy way to verify the logic is to test with a smaller example. If a clock struck 2 times, there would be 1 interval between them. If that interval was 6 seconds, then the time between the first and second strike would be 6 seconds. Extending this pattern, for 3 strikes we would have 2 intervals, taking 2 * 6 = 12 seconds, and so on. This pattern is linear in the number of intervals and confirms that using 11 intervals for 12 strikes is correct.

Why Other Options Are Wrong:
55 seconds: This would correspond to a per interval time of 5 seconds for 11 intervals, which contradicts the 30 second figure at 6 o clock.

36 seconds: This equals 6 intervals of 6 seconds each, but 12 strikes require 11 intervals, not 6.

24 seconds: Much too small and would require an unrealistically short interval between strikes compared with the given data.

60 seconds: This would correspond to 10 intervals of 6 seconds each, which is still short of the required 11 intervals.

Common Pitfalls:
The most common mistake is to equate the number of strikes directly with the number of intervals, forgetting that n strikes create only n minus 1 gaps. Students may also mistakenly compute interval time as 30 / 6 instead of 30 / 5. Keeping track of intervals instead of just counts helps ensure accurate calculations.

Final Answer:
At 12 o clock, the clock will take 66 seconds to strike 12 times.