Pariksha SaathiTime, Speed and Distance Questions with Solutions
Time, Speed and Distance is one of the most frequently tested Quant topics across these exams — and most marks lost here come from just two traps: forgetting to convert units, and averaging two speeds the wrong way. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- Speed = Distance / Time. Rearranged: Distance = Speed × Time, and Time = Distance / Speed.
- To convert km/hr to m/s, multiply by 5/18. To convert m/s to km/hr, multiply by 18/5.
- When the same distance is covered at two different speeds (for example, going and returning by the same route), the average speed for the whole journey is NOT the simple average of the two speeds — it is 2ab/(a + b). Using (a + b)/2 here is the single most common mistake in this topic.
- For two objects moving toward each other, relative speed is the sum of their speeds. For two objects moving in the same direction, relative speed is the difference of their speeds.
Worked examples
1. A car travels at a constant speed of 60 km/hr. How long will it take to cover 180 km?
Solution
- Time = Distance / Speed
- = 180 / 60
- = 3 hours
Answer: 3 hours
2. Convert a speed of 72 km/hr into metres per second.
Solution
- To convert km/hr to m/s, multiply by 5/18.
- 72 × 5/18 = 360/18
- = 20 m/s
Answer: 20 m/s
3. A man travels from town A to town B at 40 km/hr, and returns from B to A by the same road at 60 km/hr. Find his average speed for the entire journey.
Solution
- The distance each way is the same, so the simple average (40 + 60)/2 = 50 km/hr is WRONG here — that shortcut only works when the TIME spent at each speed is equal, not the distance.
- For two equal distances covered at speeds a and b, average speed = 2ab / (a + b).
- = (2 × 40 × 60) / (40 + 60)
- = 4,800 / 100 = 48 km/hr
Answer: 48 km/hr
4. Two trains, 150 m and 100 m long, run on parallel tracks in opposite directions at 45 km/hr and 36 km/hr respectively. In how much time will they completely cross each other?
Solution
- Moving in opposite directions, relative speed = sum of speeds = 45 + 36 = 81 km/hr.
- Convert to m/s: 81 × 5/18 = 22.5 m/s.
- To completely cross each other, together they must cover a distance equal to the sum of both train lengths: 150 + 100 = 250 m.
- Time = Distance / Speed = 250 / 22.5 = 100/9 ≈ 11.1 seconds.
Answer: 100/9 seconds ≈ 11.1 seconds
Try these yourself
Work through these the same way, then check against the answer.
1. A cyclist covers 150 km in 6 hours. Find his speed in km/hr.
Answer: 25 km/hr
2. Convert a speed of 90 km/hr into metres per second.
Answer: 25 m/s
3. A train covers a certain distance at 50 km/hr and returns over the same route at 75 km/hr. Find its average speed for the whole trip.
Answer: 60 km/hr
Where this comes up
Time, Speed and Distance is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and train and boat-and-stream variations show up often in the higher-difficulty papers.
Practice more Time, Speed and Distance questions
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