Half the distance at each speed — Aptitude Question
Half the distance at each speed: A man covers half a journey at 30 km/h and the other half at 20 km/h, taking 10… Answer and worked solution on CodeKairo.
- Topic: Time, Speed & Distance
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 105 seconds
Question
A man covers half a journey at 30 km/h and the other half at 20 km/h, taking 10 hours in all. What is the total distance?
Options
- 200 km
- 220 km
- 240 km
- 260 km
Show the answer and the worked solution
Correct answer: C. 240 km
Worked solution
- (d/2)/30 + (d/2)/20 = 10 → d/60 + d/40 = 10.
- Common denominator 120: 2d/120 + 3d/120 = 10 → 5d/120 = 10.
- d = 240, so the journey is 240 km.
Answer: 240 km.
The idea
Write the time for each half in terms of the whole distance and add. The average speed here is 24 km/h, and 24 × 10 = 240 confirms it.
Shortcut. Back-substitute: 240 km means 120 km at 30 km/h (4 h) plus 120 km at 20 km/h (6 h) — exactly 10 h.
Common trap. Averaging the speeds to 25 km/h gives 25 × 10 = 250 km; with equal distances the average speed is the harmonic mean, 2 × 30 × 20 ÷ 50 = 24 km/h, and that is the speed to multiply by the 10 hours.