If the 30th highest hourly volume is adopted for design, there will be congestion on road for only:
- A0 hours in a year
- B70 hours in a year
- C30 hours in a year
- D29 hours in a yearCorrect
Solution
Concept
If the 30th highest hourly volume is the design volume, traffic exceeds the design value only in the 29 hours that are higher.
Formula
Hours of congestion = 30 - 1 = 29 hours per year
Step-by-step solution
1. Arrange the 8760 hourly volumes of the year in decreasing order. 2. The design hourly volume is the 30th highest value. 3. Only the 29 hours ranked above it have more traffic than the design volume. 4. So the road is congested for only 29 hours in a year. 5. Answer: (D).
Explanation
The road is designed to carry the 30th highest hourly volume. Only the 29 hours with higher volume will exceed this capacity. This gives an economical design with very little congestion.
Why the other options are wrong
A: Zero congestion would need design for the highest hourly volume, which is uneconomical. B: 70 hours has no basis in this concept. C: In the 30th hour itself, volume equals the design volume, so it is not congested.
Shortcut
Nth highest hourly volume gives (N - 1) hours of congestion.
Common mistake
Choosing 30 hours and forgetting that the 30th hour itself equals the design volume.
Correct answer: D) 29 hours in a year