UPSC Prelims 2010 Q66: Science & Technology – Quantitative Aptitude
A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on foot
at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much
distance did he travel on foot ?
- (a) 10 km
- (b) 20 km
- (c) 30 km
- (d) 40 km
Answer: (b) 20 km
Explanation
Splitting a journey between walking and cycling
Total distance 50 km in 8 hours, part on foot at 4 km/h, part on bicycle at 10 km/h.
| Step | Calculation |
|---|---|
| Let foot distance = x km | Cycling distance = (50 − x) km |
| Time equation | x/4 + (50−x)/10 = 8 |
| Multiply through by 20 | 5x + 2(50−x) = 160 |
| Expand | 5x + 100 − 2x = 160 → 3x = 60 |
| Solve | x = 20 km |
Verification:
| Mode | Distance | Time |
|---|---|---|
| Foot | 20 km | 20/4 = 5 hours |
| Bicycle | 30 km | 30/10 = 3 hours |
Total time = 5 + 3 = 8 hours ✓
Answer: (b) 20 km.
Why each option is right or wrong
- (a) Incorrect. 10 km on foot does not satisfy the total time equation when checked.
- (b) CORRECT. Solving the time equation gives 20 km walked, verified by the 5+3 = 8 hour split.
- (c) Incorrect. 30 km on foot would require more time than the total 8 hours allows.
- (d) Incorrect. 40 km on foot would far exceed the available 8 hours at a 4 km/h walking pace.
Key point
Setting up x/4 + (50−x)/10 = 8 and solving gives x = 20 km walked (at 4 km/h, taking 5 hours) and 30 km cycled (at 10 km/h, taking 3 hours) — totaling 8 hours.
Remember
50 km in 8 hours, part at 4 km/h and part at 10 km/h: solving gives 20 km walked, 30 km cycled.
Common mistakes
- Setting up the time equation incorrectly, mixing up which variable represents which mode.
- Making an arithmetic error while clearing fractions in the equation.
- Forgetting to verify the final answer against the total time constraint.
Exam tip
For mixed-speed journey problems, set total distance as x + (total−x), write the time equation, then always verify by plugging back in.
Sources
- NCERT Class VIII Mathematics — Linear Equations in One Variable
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)