The speeds of three cars are in the ratio 2 : 3 : 5. For the same distance, what is the ratio of their times taken?
Aptitude
Time and Distance
Difficulty: Easy
Choose an option
Answer
Correct Answer: 15 : 10 : 6
Explanation
Introduction / Context:For equal distances, time is inversely proportional to speed. Given a speed ratio, the time ratio is the inverse of those numbers.
Given Data / Assumptions:
- Speed ratio = 2 : 3 : 5.
- All travel the same distance.
Concept / Approach:Time ∝ 1/speed, so time ratio = 1/2 : 1/3 : 1/5. Multiply by the LCM (30) to get whole numbers.
Step-by-Step Solution:
1/2 : 1/3 : 1/5 → multiply by 30.Times = 15 : 10 : 6.Verification / Alternative check:Check intuition: the fastest car (5 parts) should have the smallest time (6 parts), which it does.
Why Other Options Are Wrong:They place larger time for faster cars or mismatch the inverse relationship entirely.
Common Pitfalls:Forgetting to invert ratios; accidentally copying the same 2:3:5 order for times.
Final Answer:15 : 10 : 6