Practice Questions
Concept Explanation
Average speed = Total distance / Total time
It is NOT the simple average of speeds unless equal distances are covered at each speed.
Key Formulas
- Total time = d₁/s₁ + d₂/s₂ + ...
- Equal distances at speeds a and b: average speed = 2ab/(a + b)
- Round trip same distance at a and b: average speed = 2ab/(a + b)
Common Trap
60 km at 40 km/h and 60 km at 60 km/h → average speed = 120/2.5 = 48 km/h, not 50 km/h.
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Q1 Medium
A car covers 60 km at 40 km/h and 60 km at 60 km/h. Average speed for the whole journey is:
ExplanationTotal distance = 120 km. Total time = 1.5 + 1 = 2.5 hr. Average speed = 120/2.5 = 48 km/h. -
Q2 Medium
A person walks 10 km at 4 km/h and 10 km at 5 km/h. Average speed is:
ExplanationTotal time = 2.5 + 2 = 4.5 hr. Average = 20/4.5 = 4.44 km/h (approx). -
Q3 Easy
Equal distances at 30 km/h and 60 km/h. Average speed is:
Explanation2×30×60/(30+60) = 3600/90 = 40 km/h. -
Q4 Medium
A train goes from A to B at 50 km/h and returns at 75 km/h. Average speed for the round trip is:
Explanation2×50×75/(50+75) = 7500/125 = 60 km/h. -
Q5 Easy
Total distance 180 km covered in 3 hours. Average speed is:
Explanation180/3 = 60 km/h. -
Q6 Medium
40 km at 20 km/h and 60 km at 30 km/h. Average speed is:
ExplanationTime = 2 + 2 = 4 hr. Distance = 100 km. Average = 25 km/h. -
Q7 Easy
A cyclist rides 15 km at 10 km/h and 15 km at 15 km/h. Average speed is:
Explanation2×10×15/(10+15) = 300/25 = 12 km/h.
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Q8 Easy
Simple average of 40 km/h and 60 km/h is 50 km/h. For equal distances, actual average speed is:
ExplanationHarmonic mean 48 km/h is less than arithmetic mean 50 km/h for equal distances. -
Q9 Hard
100 km at 25 km/h and 100 km at 50 km/h. Average speed is:
Explanation2×25×50/(25+50) = 2500/75 = 33.33 km/h (approx). -
Q10 Medium
A car travels 2 hours at 60 km/h and 3 hours at 40 km/h. Average speed is:
ExplanationDistance = 120 + 120 = 240 km. Time = 5 hr. Average = 48 km/h. -
Q11 Easy
Equal distances at 20 km/h and 30 km/h. Average speed is:
Explanation2×20×30/(20+30) = 1200/50 = 24 km/h. -
Q12 Medium
30 km at 45 km/h and 30 km at 90 km/h. Average speed is:
Explanation2×45×90/(45+90) = 8100/135 = 60 km/h. -
Q13 Medium
A journey: 50 km at 25 km/h, 50 km at 50 km/h. Average speed is:
ExplanationTotal 100 km in 2 + 1 = 3 hr. Average = 100/3 = 33.33 km/h (approx). -
Q14 Easy
Which formula gives average speed for equal distances at speeds a and b?
ExplanationFor equal distances, average speed = harmonic mean = 2ab/(a + b).
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DS1 Easy
What is the average speed?
Statement ITotal distance is 120 km and total time is 2.5 hours.
Statement IIThe journey has two equal 60 km parts at 40 and 60 km/h.
ExplanationEach statement alone gives average speed = 120/2.5 = 48 km/h. -
DS2 Medium
What is the average speed for equal distances?
Statement IFirst part speed is 30 km/h.
Statement IISecond part speed is 60 km/h.
ExplanationNeed both speeds. Average = 2×30×60/90 = 40 km/h.
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DS3 Easy
Is average speed less than 50 km/h?
Statement IEqual distances covered at 40 km/h and 60 km/h.
Statement IITotal distance is 120 km.
ExplanationStatement I alone: average = 48 km/h < 50 km/h. -
DS4 Hard
What is the total time taken?
Statement IDistance is 100 km at 25 km/h and 100 km at 50 km/h.
Statement IIAverage speed is 33.33 km/h.
ExplanationStatement I alone: time = 4 + 2 = 6 hours.