Question

A classified vehicle count was conducted in the midblock of a two-lane one-way collector road during peak hour (08:00 A.M. - 09:00 A.M.) on a weekday. The vehicle counts and corresponding passenger car unit (PCU) are shown in the table below. If the maximum design capacity per lane of that road is 1300 PCU/hr, then the volume to capacity ratio of that road is (rounded off to two decimal places).

Vehicle Type	Hourly Vehicle Count (08:00 A.M. - 09:00 A.M.)	PCU Value
Bus	52	2.50
Truck	24	3.00
Car	720	1.00
Motorized Two-Wheeler	1050	0.50
Auto Rickshaw	275	0.80
E-Rickshaw	410	0.80
Bicycle	90	0.30

Hint:

Convert each vehicle count to PCU by multiplying with its PCU factor, sum for total volume, and divide by the road's total capacity (capacity per lane x number of lanes).

Answer 1

Correct Answer: 0.78

Step 1: Understanding the Question.
We are given the hourly count of each vehicle type on a two-lane, one-way collector road, along with the Passenger Car Unit (PCU) factor for each type. We must convert the mixed traffic into a single PCU volume, then compare it against the road's total design capacity to get the volume to capacity (V/C) ratio.

Step 2: Recall the PCU concept.
The PCU value converts each vehicle type into an equivalent number of passenger cars, based on how much road space and disturbance it causes. Multiplying each vehicle's hourly count by its PCU factor gives that vehicle type's contribution to the total traffic volume, in PCU/hr.

Step 3: Compute the PCU volume for each vehicle type.
\[ Bus: 52 \times 2.50 = 130 \]
\[ Truck: 24 \times 3.00 = 72 \]
\[ Car: 720 \times 1.00 = 720 \]
\[ Motorized\ Two\text{-}Wheeler: 1050 \times 0.50 = 525 \]
\[ Auto\ Rickshaw: 275 \times 0.80 = 220 \]
\[ E\text{-}Rickshaw: 410 \times 0.80 = 328 \]
\[ Bicycle: 90 \times 0.30 = 27 \]

Step 4: Add these up to get the total traffic volume.
\[ V = 130+72+720+525+220+328+27 = 2022\ \text{PCU/hr} \]

Step 5: Work out the total design capacity of the road.
The capacity given, \(1300\ PCU/hr\), is per lane, and the road is a two-lane road (both lanes carrying one-way traffic), so the total capacity of the road is:
\[ C = 2 \times 1300 = 2600\ \text{PCU/hr} \]

Step 6: Compute the volume to capacity ratio.
\[ \frac{V}{C} = \frac{2022}{2600} = 0.7777\ldots \]
Rounded off to two decimal places, as the question asks:

Final Answer:
The volume to capacity ratio of the road is about 0.78, which lies inside the accepted range of 0.72 to 0.85.
\[ \boxed{V/C \approx 0.78} \]