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Time, speed and distance practice questions for bank exams
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Time, speed and distance (TSD) rests on one relation: distance equals speed multiplied by time. Questions dress it up with trains crossing platforms, two travellers meeting, a round trip at two speeds, or a late arrival. The skill is converting units correctly and choosing between relative speed and plain speed. The five questions below cover the types that repeat in bank-exam Quant.
Formulas and conversions
| Idea | Rule |
|---|---|
| Basic relation | Distance = speed × time |
| km/h to m/s | Multiply by 5/18 (54 km/h = 15 m/s) |
| Same distance at two speeds | Average speed = 2ab ÷ (a + b) |
| Equal distance | Speeds and times are in inverse ratio |
| Two objects moving towards each other | Relative speed = sum of speeds |
| Two objects moving in the same direction | Relative speed = difference of speeds |
| Train crossing a pole or person | Length ÷ relative speed |
| Train crossing a platform or another train | Sum of lengths ÷ relative speed |
Five practice questions
Question 1
A train 120 m long is running at 54 km/h. How long will it take to cross a platform 180 m long?
- A. 12 seconds
- B. 16 seconds
- C. 18 seconds
- D. 20 seconds
Question 2
A man travels from his home to his office at 60 km/h and returns at 40 km/h. What is his average speed for the whole journey?
- A. 45 km/h
- B. 48 km/h
- C. 50 km/h
- D. 52 km/h
Question 3
A starts from P at 6 am towards Q at 40 km/h. B starts from Q at 8 am towards P at 50 km/h. The distance between P and Q is 440 km. At what time do they meet?
- A. 11:00 am
- B. 11:30 am
- C. 12:00 noon
- D. 12:30 pm
Question 4
A 150 m long train running at 72 km/h overtakes a cyclist who is riding in the same direction at 18 km/h. How long does it take to pass the cyclist?
- A. 10 seconds
- B. 12 seconds
- C. 15 seconds
- D. 18 seconds
Question 5
A man covers a distance at 12 km/h and reaches 20 minutes late. At 15 km/h he reaches 10 minutes early. What is the distance?
- A. 24 km
- B. 30 km
- C. 36 km
- D. 40 km
Answers and explanations
- D. 54 km/h = 54 × 5/18 = 15 m/s. The train must cover its own length plus the platform: 120 + 180 = 300 m. The time is 300 ÷ 15 = 20 seconds.
- B. For equal distances, the average speed is the harmonic mean: 2 × 60 × 40 ÷ (60 + 40) = 4,800 ÷ 100 = 48 km/h. The simple mean 50 is the trap.
- C. By 8 am, A has covered 2 × 40 = 80 km, leaving 360 km. They then close the gap at 40 + 50 = 90 km/h, which takes 360 ÷ 90 = 4 hours. They meet at 12:00 noon. Check: A has gone 240 km and B 200 km, and 240 + 200 = 440.
- A. 72 km/h = 20 m/s and 18 km/h = 5 m/s. The relative speed is 15 m/s, and the train must cover only its own length: 150 ÷ 15 = 10 seconds.
- B. The time difference is 20 + 10 = 30 minutes = 0.5 hours. So d ÷ 12 − d ÷ 15 = 0.5, which gives d × (5 − 4) ÷ 60 = 0.5, so d = 30 km. Check: 30 ÷ 12 = 2.5 hours and 30 ÷ 15 = 2 hours, a gap of 0.5 hours.
How to prepare time, speed and distance
- Convert units on the first line. Decide to work in km/h and hours, or m/s and seconds, and convert everything before you calculate.
- Choose the right speed. For opposite directions add speeds, and for the same direction subtract. Say it aloud once, because swapping them is the most common error.
- Never average speeds directly. If the distance is equal, use 2ab ÷ (a + b). If the time is equal, a simple average works.
- Use inverse proportion. At equal distance, a speed ratio of 4 : 5 means a time ratio of 5 : 4. Many "usual time" questions are two-line problems this way.
- Handle delayed starts by adjusting the head start. Compute how far the early traveller has gone, then treat the remainder as a plain meeting problem (Question 3).
- Sketch it. A line with two dots and arrows takes five seconds and prevents most wrong set-ups.
Boats and streams uses the same relations with a current added, so go on to boats and streams next. A target of 45 seconds per question is fair for standard types.
The full time, speed and distance topic test is on PrepMatic (about 15 questions, 30 minutes). The Quantitative Aptitude guide places TSD among the other Quant topics, and the bank exam hub has each exam's pattern.
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