The speeds of two cars are in the ratio 7 : 8. If the second car covers 200 km in 5 hours (i.e., 40 km/h), find the speed of the first car (in km/h).
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 35 km/h
Explanation
Introduction / Context:Speed ratios scale actual speeds by a common factor. Once you identify the common factor from one car, you can compute the other car’s speed directly.
Given Data / Assumptions:
- Speed ratio (Car1 : Car2) = 7 : 8.
- Car2 speed = 200 / 5 = 40 km/h.
Concept / Approach:If 8 parts correspond to 40 km/h, then 1 part is 40/8, and 7 parts (Car1) give the required speed.
Step-by-Step Solution:
Common factor = 40 / 8 = 5 km/h per part.Car1 speed = 7 × 5 = 35 km/h.Verification / Alternative check:Proportion: 35 : 40 simplifies to 7 : 8, matching the ratio.
Why Other Options Are Wrong:28, 25, 32, 40 km/h do not maintain the 7 : 8 proportion with a 40 km/h second car.
Common Pitfalls:Confusing the mapping of “7” and “8” to the first/second car; not simplifying to get the correct scale factor.
Final Answer:35 km/h