If a man starts at 7 a.m. at \(\frac{5}{4}\) of his usual speed, he reaches his office 30 minutes earlier than usual. At what time does he reach his office at the new speed?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9 a.m.
For a fixed distance, time is inversely proportional to speed: at \(\frac{5}{4}\) of the usual speed the journey takes \(\frac{4}{5}\) of the usual time. The time saved is therefore \(\frac{1}{5}\) of the usual time, and that is the given 30 minutes.
\(\frac{1}{5}\) of the usual time \(=30\) min, so the usual time \(=150\) min (2 h 30 min)
Time at the new speed \(=150-30=120\) min (2 h)
Starting at 7 a.m., he reaches at \(7+2=9\) a.m.