# Calculating Cost per Passenger-Km or Tonne-Km

## Standard 4-Step Procedure

Step 1: Calculate total cost incurred per month or per year (sum of fixed + variable + semi-variable).

Step 2: Calculate total kms travelled.

Step 3: Calculate total passenger-kms or total tonne-kms.

Step 4: Cost per passenger-km (or tonne-km) =

$$\frac{\text{Total Cost (Step 1)}}{\text{Total Passenger-Km or Tonne-Km (Step 3)}}$$

## When the Number of Passengers Changes Along the Route

If the number of passengers/tonnes carried varies between different stations, you must calculate passenger-kms for each segment separately and then add them up.

## Formula

$$\text{Passenger-Km for a segment} = \text{No. of passengers in that segment} \times \text{Distance of that segment}$$

Then total them across all segments.

Worked example

### Example 1

Example: Passenger-Km on a Triangular Route

A bus runs on the route X → Y → Z → X with:

X to Y: 400 km, carrying 100 passengers
Y to Z: 300 km, carrying 120 passengers
Z to X: 150 km, carrying 70 passengers

Calculation:

Segment	Distance	Passengers	Passenger-Km
X → Y	400 km	100	40,000
Y → Z	300 km	120	36,000
Z → X	150 km	70	10,500
Total			86,500 passenger-km

If total cost is, say, ₹1,73,000, then cost per passenger-km = 1,73,000 / 86,500 ≈ ₹2 per passenger-km.

⚠️ Common exam mistakes

Multiplying total passengers by total distance instead of segment-wise calculation when passenger load changes
Forgetting to sum passenger-kms across all segments of the route
Confusing kms travelled with passenger-kms — they are different denominators for different calculations

Reference:

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Calculating Cost per Passenger-Km / Tonne-Km

Worked example

⚠️ Common exam mistakes