A clock strikes as many times as the hour at each full hour (4 times at 4 o’clock, and so on), with equal gaps between the strikes. It takes 9 seconds to strike 4 at 4 o’clock, timed from the first strike to the last. How long will it take to strike 10 at 10 o’clock?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 27 seconds
The time is taken up by the gaps between strikes, not by the strikes themselves. A clock striking \(n\) times leaves \(n-1\) gaps between the first strike and the last.
4 strikes leave \(4-1=3\) gaps, which take 9 seconds
One gap \(=\displaystyle\frac{9}{3}=3\) seconds
10 strikes leave \(10-1=9\) gaps
Time \(=9\times3=27\) seconds
Why the other options are incorrect
Option (1) 22.5 seconds — Incorrect. This divides 9 seconds among the 4 strikes instead of the 3 gaps: \(\frac{9}{4}\times10\).
Option (2) 24 seconds — Incorrect. This is 8 gaps of 3 seconds; 10 strikes leave 9 gaps, not 8.
Option (4) 30 seconds — Incorrect. This counts 10 gaps of 3 seconds, one for each strike.