UPSC Prelims 2002 Q91: Science & Technology – Quantitative Aptitude
Two ladies simultaneously leave cities A and B connected by a straight road and travel
towards each other. The first lady travels 2 km/hr faster than the second lady and reaches B one
hour before the second lady reaches
A. The two cities A and B are 24 km apart. How many kilometres does each lady travel in one
hour?
- (a) 5 km, 3 km
- (b) 7 km, 5 km
- (c) 8 km, 6 km
- (d) 16 km, 14 km
Answer: (c) 8 km, 6 km
Explanation
Speeds of two ladies travelling towards each other
| Step | Working |
|---|---|
| Let the second lady's speed be x km/h | The first lady's speed is x + 2 km/h |
| Distance | 24 km each |
| Time difference | 24/x − 24/(x + 2) = 1 hour |
| Solve | 48 = x(x + 2), so x = 6; the speeds are 8 km/h and 6 km/h |
The first lady, being faster by 2 km/h, takes one hour less for the 24 km. From 24/x − 24/(x + 2) = 1 we get x² + 2x − 48 = 0, so x = 6. The ladies travel 8 km and 6 km in one hour.
Answer: (c) 8 km, 6 km.
Why each option is right or wrong
- (a) Incorrect. At 5 and 3 km/h the time gap is 3.2 hours.
- (b) Incorrect. At 7 and 5 km/h the gap is about 1.37 hours.
- (c) CORRECT. 24/6 = 4 hours and 24/8 = 3 hours, a gap of one hour.
- (d) Incorrect. At 16 and 14 km/h the gap is about 0.2 hour.
Key point
Time gap = distance ÷ slower speed − distance ÷ faster speed.
Remember
24/6 − 24/8 = 4 − 3 = 1 hour.
Common mistakes
- Using the sum of the distances (48 km) in the time-gap equation.
- Not forming the quadratic and guessing.
- Missing that the speed difference is 2 km/h.
Exam tip
Test the options: only 8 and 6 give 3 hours and 4 hours.
Sources
- NCERT Class X Mathematics — Quadratic equations
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Time and Distance)