The speeds of a car, a train and a bus are in the ratio 5 : 9 : 4. The combined average speed of the car, the bus and the train is 72 km/h. What is the average speed of the car and the train taken together?

Introduction / Context:
This question involves speed ratios and average speed of multiple vehicles. We first determine individual speeds from the ratio using the given combined average, then compute the average of two selected vehicles.

Given Data / Assumptions:
- Speed ratio (car : train : bus) = 5 : 9 : 4.
- Combined average speed of all three = 72 km/h.
- All speeds are in km/h.
- The average of the three is the simple arithmetic mean of their speeds.

Concept / Approach:
Let the common multiplying factor be k. Then the speeds are:
Car speed = 5k, Train speed = 9k, Bus speed = 4k
The average speed of the three is:
(5k + 9k + 4k) / 3 = 18k / 3 = 6k
We equate 6k to 72 to find k and then determine the speeds of the car and train, and their average.

Step-by-Step Solution:
Step 1: Let speeds be 5k, 9k and 4k as per the ratio.Step 2: Average speed of three = (5k + 9k + 4k) / 3 = 18k / 3 = 6k.Step 3: Given 6k = 72, so k = 72 / 6 = 12.Step 4: Car speed = 5k = 5 * 12 = 60 km/h.Step 5: Train speed = 9k = 9 * 12 = 108 km/h.Step 6: Average speed of car and train together = (60 + 108) / 2 = 168 / 2 = 84 km/h.

Verification / Alternative check:
Check the bus speed: 4k = 4 * 12 = 48 km/h. The average of 60, 108 and 48 is (60 + 108 + 48) / 3 = 216 / 3 = 72 km/h, which matches the given combined average, confirming that the scaling factor and individual speeds are correct.

Why Other Options Are Wrong:
- 96 km/h and 72 km/h do not match the computed average of car and train speeds, which is 84 km/h.
- 60 km/h is the speed of the car alone, not the average of car and train.

Common Pitfalls:
- Mixing up the ratio or assigning incorrect coefficients to car, train and bus.
- Averaging the three given speeds incorrectly or using weighted averages where simple means are intended.
- Forgetting that the given 72 km/h is the mean of three individual speeds, not of distances or times.

Final Answer:
The average speed of the car and the train together is 84 km/h.