The speed ratio of a car, a train, and a bus is 5 : 9 : 4. If their average speed taken together is 72 km/h, what is the average speed of the car and the train together?

Introduction / Context:
Convert the ratio to concrete speeds using the given combined average. Then compute the simple average for the subset (car and train).

Given Data / Assumptions:

• Car:Train:Bus = 5:9:4 ⇒ let speeds be 5k, 9k, 4k.
• Average of all three = (5k + 9k + 4k)/3 = 72 ⇒ 6k = 72.

Concept / Approach:
Solve k, then compute car and train speeds and take their mean.

Step-by-Step Solution:

Verification / Alternative check:
Bus would be 48 km/h; the mean of all three is (60 + 108 + 48)/3 = 72—consistent.

Why Other Options Are Wrong:
78 or 82 km/h do not follow from k = 12; “Cannot be determined” is false because the ratio plus average is sufficient.

Common Pitfalls:
Averaging the ratio numbers directly without solving for k.

Final Answer:
84 km/h