Average speed with two different speeds — ratio of distances: A man travels part of a journey at 20 km/h and the rest at 70 km/h. His overall average speed is 50 km/h. What is the ratio of the distance covered at 20 km/h to that covered at 70 km/h?
Aptitude
Time and Distance
Difficulty: Medium
Choose an option
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A4 : 21
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B3 : 22
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C1 : 4
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D3 : 5
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E7 : 15
Answer
Correct Answer: 4 : 21
Explanation
Introduction / Context:When average speed over a whole trip is known and the trip has only two constant-speed segments, ratios can be derived without the absolute distance.
Given Data / Assumptions:
- Speeds: v1 = 20 km/h, v2 = 70 km/h
- Average over the entire journey: V_avg = 50 km/h
- Let distances be d1 and d2 for the two legs.
Concept / Approach:Average speed V_avg = (d1 + d2) / (d1/20 + d2/70). Let x = d1/d2 and solve for x.
Step-by-Step Solution:
(x + 1) / (x/20 + 1/70) = 50Denominator = (7x + 2)/140 ⇒ ratio = 140(x + 1)/(7x + 2)140x + 140 = 50(7x + 2) = 350x + 100⇒ 210x = 40 ⇒ x = 4/21Verification / Alternative check:Try d1 : d2 = 4 : 21 with any scaling; average recomputes to 50 km/h.
Why Other Options Are Wrong:Other ratios fail to satisfy the average speed relationship.
Common Pitfalls:Using time ratios instead of distance ratios in the average speed formula.
Final Answer:4 : 21