Time, Speed & Distance
Quick Recap
- Speed = Distance / Time
- Distance = Speed × Time
- Time = Distance / Speed
- To convert km/h to m/s, multiply by 5/18.
- To convert m/s to km/h, multiply by 18/5.
- Relative speed in opposite direction = sum of speeds.
- Relative speed in same direction = difference of speeds.
- Average speed for equal distances = 2xy / (x + y).
- Upstream speed = Boat speed – Stream speed.
- Downstream speed = Boat speed + Stream speed.
Q1. A train leaves station A at 4 pm and reaches station B at 5:15 pm. Another train leaves station B at 4:45 pm and reaches station A at 5:30 pm. At what time do they cross each other?
Correct Option: E
Rationale:
First train takes 75 minutes for the journey.
Second train takes 45 minutes for the journey.
By 4:45 pm, first train has travelled 45/75 = 3/5 of the distance.
Remaining gap = 2/5.
Relative speed = 1/75 + 1/45 = 8/225 of the distance per minute.
Meeting time after 4:45 pm:
(2/5) ÷ (8/225) = 11.25 minutes = 11 min 15 sec
They meet at 4:56:15 pm.
Q2. A train of length 100 metres is moving at 72 km/h. A man is walking in the same direction at 6 km/h. How much time will the train take to completely pass the man?
Correct Option: B
Rationale:
Relative speed = 72 – 6 = 66 km/h
66 km/h = 66 × 5/18 = 55/3 m/s
Time = 100 ÷ 55/3
= 300/55
= 60/11
= 5.45 seconds approximately.
Q3. A train 150 m long is running at 54 km/h. It crosses a bridge in 20 seconds. Find the length of the bridge.
Correct Option: C
Rationale:
Speed = 54 × 5/18 = 15 m/s
Total distance crossed in 20 seconds:
15 × 20 = 300 m
Bridge length = 300 – train length
= 300 – 150
= 150 m.
Q4. A train crosses a pole in 8 seconds. If the length of the train is 200 metres, find the speed of the train.
Correct Option: C
Rationale:
Speed = Distance / Time
= 200/8
= 25 m/s
Convert to km/h:
25 × 18/5 = 90 km/h.
Q5. A and B are two stations 480 km apart. A train starts from A at 9:30 am and travels towards B at 72 km/h. Another train starts from B at 10:15 am and travels towards A at 48 km/h. At what time do the trains meet?
Correct Option: C
Rationale:
First train travels alone from 9:30 am to 10:15 am = 45 minutes = 3/4 hour.
Distance covered = 72 × 3/4 = 54 km
Remaining distance = 480 – 54 = 426 km
Relative speed = 72 + 48 = 120 km/h
Time after 10:15 am:
426/120 = 3.55 hours = 3 hours 33 minutes
Meeting time = 1:48 pm.
Q6. Train A, 600 metres long, is running at 80 km/h. How much time will it take to cross a man sitting in another train running at 64 km/h in the opposite direction?
Correct Option: C
Rationale:
Relative speed = 80 + 64 = 144 km/h
144 km/h = 40 m/s
Only the 600 m train has to cross the man.
Time = 600/40 = 15 seconds.
Q7. Two trains, 130 m and 110 m long, are moving in the same direction. The faster train takes one minute to pass the other completely. If they move in opposite directions, they pass each other completely in 3 seconds. Find the speeds of the faster and slower trains respectively.
Correct Option: A
Rationale:
Total length = 130 + 110 = 240 m
Same direction:
Relative speed = 240/60 = 4 m/s
Opposite direction:
Relative speed = 240/3 = 80 m/s
Let faster speed = F and slower speed = S.
F – S = 4
F + S = 80
Solving:
F = 42 m/s, S = 38 m/s.
Q8. A man is sitting in a train moving at 50 km/h. He observes that a goods train travelling in the opposite direction takes 9 seconds to pass him completely. If the goods train is 280 metres long, find its speed.
Correct Option: B
Rationale:
Relative speed = 280/9 m/s
Convert to km/h:
280/9 × 18/5 = 112 km/h
Since trains move in opposite directions:
Goods train speed + 50 = 112
Goods train speed = 62 km/h.
Q9. A jogger running at 9 km/h alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 km/h in the same direction. In how much time will the train completely pass the jogger?
Correct Option: A
Rationale:
Relative speed = 45 – 9 = 36 km/h = 10 m/s
Train must cover:
Initial gap + train length = 240 + 120 = 360 m
Time = 360/10 = 36 seconds.
Q10. If the speed of a boat in still water is 8 km/h and the speed of the stream is 4 km/h, what is the upstream speed of the boat?
Correct Option: D
Rationale:
Upstream speed = Speed in still water – Stream speed
= 8 – 4
= 4 km/h.
Q11. A boat travels 10 km upstream in 30 minutes and the same distance downstream in 25 minutes. What is the speed of the river current?
Correct Option: B
Rationale:
Upstream speed = 10 ÷ 30/60 = 20 km/h
Downstream speed = 10 ÷ 25/60 = 24 km/h
Stream speed = (Downstream speed – Upstream speed) / 2
= (24 – 20) / 2
= 2 km/h.
Q12. A person walks at 5 km/h for 10 hours. What is the distance travelled by him?
Correct Option: A
Rationale:
Distance = Speed × Time
= 5 × 10
= 50 km.
Q13. In a 200 m race, A beats B by 5 seconds and B beats C by 7 seconds. By how many seconds does A beat C?
Correct Option: E
Rationale:
A beats B by 5 seconds.
B beats C by 7 seconds.
So A beats C by:
5 + 7 = 12 seconds.
Q14. A rabbit takes 6 hops while a dog takes 5 hops in the same time. If 4 hops of the dog equal 5 hops of the rabbit, what is the ratio of their speeds (Rabbit : Dog)?
Correct Option: C
Rationale:
Speed is proportional to number of hops × length of each hop.
Rabbit : Dog = 6R : 5D
Given:
4D = 5R
D = 5R/4
So:
Rabbit : Dog = 6R : 5 × 5R/4
= 6R : 25R/4
= 24 : 25.
Q15. In a 100 m race, A runs at a speed of 8 km/h. A gives B a start of 4 m and still beats him by 15 seconds. What is the speed of B?
Correct Option: C
Rationale:
A’s speed = 8 km/h = 20/9 m/s
Time taken by A for 100 m:
100 ÷ 20/9 = 45 seconds
B gets a 4 m start, so B runs 96 m.
A still beats B by 15 seconds, so B takes:
45 + 15 = 60 seconds
B’s speed = 96/60 = 1.6 m/s
= 1.6 × 18/5 = 5.76 km/h
≈ 5.8 km/h.
Q16. A motorist travels to a place 150 km away at an average speed of 50 km/h and returns at 30 km/h. What is his average speed for the whole journey?
Correct Option: C
Rationale:
For equal distances, average speed:
= 2xy / (x + y)
= 2 × 50 × 30 / (50 + 30)
= 3000 / 80
= 37.5 km/h.
Q17. A person covers half of his journey at 30 km/h, one-third at 40 km/h and the remaining part at 20 km/h. What is his average speed for the whole journey?
Correct Option: D
Rationale:
Let total distance = 1.
Time taken:
(1/2)/30 + (1/3)/40 + (1/6)/20
= 1/60 + 1/120 + 1/120
= 1/30 hour
Average speed = Total distance / Total time
= 1 ÷ 1/30
= 30 km/h.
Q18. A man travels three equal distances at speeds of 30 km/h, 40 km/h and 60 km/h respectively. What is his average speed for the entire journey?
Correct Option: A
Rationale:
For three equal distances:
Average speed = 3 / (1/30 + 1/40 + 1/60)
LCM = 120
1/30 + 1/40 + 1/60 = 4/120 + 3/120 + 2/120 = 9/120 = 3/40
Average speed = 3 ÷ 3/40 = 40 km/h.
Time, Speed and Distance Questions for CET 2026 Quant Preparation
Time, Speed and Distance is one of the most important arithmetic topics for CET 2026, MBA entrance exams, banking exams, aptitude tests and placement preparation. This topic includes trains, boats and streams, roads and races, relative speed, average speed, meeting time, crossing time and unit conversion. Students must be comfortable converting km/h into m/s, calculating relative speed in the same or opposite direction, solving train length questions and applying average speed formulas for equal and unequal distances. Regular practice of Time, Speed and Distance questions improves speed, accuracy and logical thinking in the Quant section. These problems often appear in CET, CMAT, CAT, SNAP, NMAT, Bank PO, SSC and campus recruitment exams. This quiz provides step-by-step solutions so learners can understand the method behind every answer. Use this practice module to strengthen formulas, avoid common mistakes and improve confidence for high-scoring CET 2026 Quant attempts.
