If a man walks to his office at 3/4th of his usual rate, he reaches office 1/3rd of an hour later than usual. How much time does he usually take to reach his office?
- 1/2 hour
- 1 hour
- 1/4 hour
- 3/2 hours
- 2/3 hour
The Usual Method
Assuming the distance between his home and office as ‘4’, his usual speed as ‘s’ and the usual time as ‘t’.
When s becomes 3/4 of s, t becomes
Hence usual time = 1 hour.
Estimated Time to arrive at the answer = 60 seconds.
Observe that by a 25% reduction in speed, the person reaches his office later by 33% of an hour. Thus by increasing speed by 33% of the present (not the usual speed), the person will take 25% of an hour less than what he took earlier (not the usual time).
Assuming t = hour. A 33% increase in speed on 3/4s, will give 1s. Thus 25% decrease of time on (t + 1/3) hours will give t hours which is the usual time. This satisfies the condition of traveling at usual speed s and also the arithmetical relationship that an increase of 33% can be brought to usual by a decrease of 25%. Thus t = 1 hour is true.
Estimated Time to arrive at the answer = 10 seconds.