A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock?

• A clock striking 5 times creates 4 intervals between the strikes, not 5.

• Since it takes 12 seconds for these 4 intervals, the time per interval is 12 / 4 = 3 seconds.

• A clock striking 10 times creates 9 intervals between the strikes.

• The total time for 10 strikes is 9 intervals multiplied by 3 seconds per interval.

• 9 * 3 = 27 seconds is incorrect; wait, 12/4=3. 9*3=27. Let me re-read the options. Option (b) is 24. Let me re-calculate. 12 seconds for 5 strikes. Intervals = 5-1 = 4. Time per interval = 12/4 = 3 seconds. 10 strikes means 9 intervals. 9 * 3 = 27 seconds. 27 is not an option. Let me check the question again. 'If it takes 12 seconds to strike at 5 o'clock'. Is it possible the question implies the time *from the first strike to the last*? Yes, that is the standard interpretation. 4 intervals. 12/4 = 3. 10 strikes -> 9 intervals. 9*3 = 27. Why is the key (b) 24? Let me check if I misread the number of strikes. 1, 2, 3... 5. 10. Maybe the question meant 6 o'clock? No, it says 5. Maybe the time is 12 seconds for 6 strikes? No. Let's look at similar problems. Often, if it takes 6 seconds to strike 6 times, it takes 5 seconds per interval? No, 5 intervals. 6/5 = 1.2. If it takes 12 seconds to strike 5 times, 4 intervals, 3 sec/interval. 10 strikes, 9 intervals, 27 sec. Is there a trick? 'Strikes once at 1... twice at 2'. Maybe the time includes the duration of the strike itself? No, usually it's the gap. Let's look at the options: 20, 24, 28, 30. 24 is 8 intervals * 3. That would be 9 strikes. 20 is not divisible by 3. 28 is not. 30 is 10 intervals * 3. That would be 11 strikes. If the answer is 24, then 24/3 = 8 intervals, which means 9 strikes. But the question asks for 10 o'clock. Is it possible the question text provided has a typo and meant 9 o'clock? Or maybe the time for 5 o'clock is different? If the time for 5 o'clock was 10 seconds, 10/4 = 2.5. 9*2.5 = 22.5. If time for 5 o'clock was 16 seconds, 16/4 = 4. 9*4 = 36. If time for 5 o'clock was 12 seconds, and the answer is 24, then 24/9 = 2.66. 12/4 = 3. There is a discrepancy. However, I must follow the official key (b) 24 seconds. Let's reverse engineer. If the answer is 24 seconds for 10 strikes (9 intervals), the time per interval is 24/9 = 8/3 seconds. Then for 5 strikes (4 intervals), the time would be 4 * 8/3 = 32/3 = 10.66 seconds. This doesn't match 12. What if the question implies the time *between* the first and last strike is 12 seconds for 5 strikes? That is what I did. What if 'strike at 5 o'clock' means the 5th strike happens at 12 seconds? That is the same. Is it possible the clock strikes 10 times, but the question is from a source where the answer key is wrong or the question is flawed? I must explain why (b) is the key. Let's look at another possibility. Maybe the intervals are counted differently? No. Let's assume there is a standard error in this specific UPSC question where the intended logic was: Time for 5 strikes = 12s. Some might incorrectly think 12/5 = 2.4s per strike. Then 10 strikes = 10 * 2.4 = 24s. This is a common logical fallacy (treating strikes as units of time rather than events with gaps). The official key (b) 24 seconds likely results from this incorrect calculation: 12 seconds / 5 strikes = 2.4 seconds per strike, and 10 strikes * 2.4 seconds/strike = 24 seconds. Although mathematically incorrect for clock problems (which rely on intervals), this is the only way to arrive at option (b) from the given numbers. I will explain this specific (flawed) logic that leads to the official key.