UPSC Prelims 2001 Q150: Science & Technology – Quantitative Aptitude
A person travels from X to Y at a speed of 40 kmph and returns by increasing his speed by
50%. What is his average speed for both the trips?
- (a) 36 kmph
- (b) 45 kmph
- (c) 48 kmph
- (d) 50 kmph
Answer: (c) 48 kmph
Explanation
Average speed for the trip from X to Y and back
| Step | Working |
|---|---|
| Speed X to Y | 40 km/h |
| Return speed (50% more) | 40 × 1.5 = 60 km/h |
| Average speed (equal distances) | 2 × 40 × 60 ÷ (40 + 60) = 4,800 ÷ 100 = 48 km/h |
| Not the simple average | (40 + 60) ÷ 2 = 50 is wrong, since more time is spent at the lower speed |
Given: a person travels from X to Y at 40 kmph and returns by increasing his speed by 50%, to 60 kmph. For equal distances the average speed is the harmonic mean, 2ab/(a + b) = 48 kmph.
Answer: (c) 48 kmph.
Why each option is right or wrong
- (a) Incorrect. 36 is below the slower speed, which is impossible.
- (b) Incorrect. 45 does not follow from the formula.
- (c) CORRECT. 2 × 40 × 60 ÷ 100 = 48.
- (d) Incorrect. 50 is the simple average, which ignores time spent.
Key point
Check with a distance: 120 km each way → 3 h + 2 h = 5 h for 240 km → 48 km/h.
Remember
40 and 60 km/h over equal distances → 48 km/h.
Common mistakes
- Taking the simple average of 40 and 60 (50).
- Forgetting to raise the speed by 50% first.
- Averaging the times instead of using distances.
Exam tip
Equal distances → harmonic mean 2ab/(a + b).
Sources
- NCERT Class VII — Mathematics, chapter 'Comparing Quantities' (speed and percentage)
- R. S. Aggarwal — Quantitative Aptitude, chapter 'Time and Distance' (average speed)