UPSC Prelims 2003 Q44: Science & Technology – Quantitative Aptitude
A car travels the first one - third of a certain distance with a speed of 10 km/hr, the next
one - third distance with a speed of 20 km/hr and the last one - third distance with a speed of 60
km/hr. The average speed of the car for the whole journey is
- (a) 18 km/hr
- (b) 24 km/hr
- (c) 30 km/hr
- (d) 36 km/hr
Answer: (a) 18 km/hr
Explanation
Average speed over three equal parts of a distance
| Part | Time for a distance d/3 (in units of d) |
|---|---|
| First third at 10 km/hr | d / 30 |
| Second third at 20 km/hr | d / 60 |
| Last third at 60 km/hr | d / 180 |
| Total time | d (6 + 3 + 1)/180 = d/18 |
The average speed is total distance divided by total time, d divided by d/18, which is 18 km/hr (the harmonic mean of the three speeds).
Answer: (a) 18 km/hr.
Why each option is right or wrong
- (a) CORRECT. 3 / (1/10 + 1/20 + 1/60) = 18.
- (b) Incorrect. 24 is not the harmonic mean of 10, 20 and 60.
- (c) Incorrect. 30 is the simple average of 10, 20 and 60 only.
- (d) Incorrect. 36 is the average of 10 and 60 ignoring time.
Key point
Equal distances: average speed is the harmonic mean; equal times: the arithmetic mean.
Remember
The average speed over equal distances is the harmonic mean, 18 km/hr.
Common mistakes
- Taking the arithmetic mean (30) of the speeds.
- Averaging only two of the three speeds.
- Forgetting that time differs on each part.
Exam tip
Equal distances at different speeds: use total distance over total time.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Time, Speed and Distance)