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: Group the vehicle types by mode category first.
Rather than adding all seven PCU values in one long row, group them into mode categories, find each group's subtotal, then add the subtotals.

Step 2: Public transport and goods vehicles.
Bus: $52 \times 2.50 = 130$
Truck: $24 \times 3.00 = 72$
Subtotal: $130 + 72 = 202$ PCU/hr

Step 3: Personalized motorized vehicles.
Car: $720 \times 1.00 = 720$
Motorized two-wheeler: $1050 \times 0.50 = 525$
Subtotal: $720 + 525 = 1245$ PCU/hr

Step 4: Intermediate public transport (IPT).
Auto rickshaw: $275 \times 0.80 = 220$
E-rickshaw: $410 \times 0.80 = 328$
Subtotal: $220 + 328 = 548$ PCU/hr

Step 5: Non-motorized transport (NMT).
Bicycle: $90 \times 0.30 = 27$ PCU/hr

Step 6: Add the four subtotals for the total volume.
\[ V = 202 + 1245 + 548 + 27 = 2022\ \text{PCU/hr} \]
This matches what a single running total would give, confirming there is no arithmetic slip.

Step 7: Divide by the two-lane capacity.
The road carries one-way traffic over two lanes, each rated at $1300$ PCU/hr, so total capacity is $2 \times 1300 = 2600$ PCU/hr.
\[ \frac{V}{C} = \frac{2022}{2600} = 0.78 \]

Step 8: Conclude.
The volume to capacity ratio, rounded to two decimal places, is about 0.78, comfortably inside the accepted band of 0.72 to 0.85.
\[ \boxed{V/C \approx 0.78} \]