Maths-6 Time and Distance: Practice Questions and Step-by-Step Solutions for Competitive Exams (SSC, BSSC, Bank, Railways)
Time & Distance — 20-question mixed worksheet (Basic → Exam) with step-by-step solutions
20 practice questions on Time, Speed & Distance, arranged easy to hard. Each problem is followed by a clear, digit-by-digit solution so you can see exactly how each number was calculated.
✅ Quick formula reminders (keep beside you)
- Distance = Speed × Time
- Speed = Distance ÷ Time
- Time = Distance ÷ Speed
- km/hr ⇄ m/s: multiply by (5/18) (km/hr → m/s) or by (18/5) (m/s → km/hr)
- When two move towards each other → relative speed = sum of speeds.
- When two move same direction → relative speed = difference of speeds.
- For equal distances at speeds (v1,v2): average speed 2v1v2/ (v1+v2).
- For different time intervals, average speed = total distance ÷ total time.
Practice Questions
Basic
1) A bike covers 120 km in 3 hours. Find its speed.
Solution:
Speed = Distance/Time}} = 120/3
Compute: 120 / 3 = 40
Answer: 40 km/h
2) Convert 54 km/hr into m/s.
Solution:
Use factor x 5/18
First compute (54 /18 = 3). Then (3 x 5 = 15).
So 54 x 5/18 = 15) m/s.
Answer: 15 m/s
3) A train 180 m long passes a pole in 12 seconds. Find its speed in km/hr.
Solution:
Speed (m/s) = 180m = 15 m/s (because (180 / 12 = 15)
Convert to km/hr: 15 x 18/5
Compute (15 x 18 = 270). Then (270/ 5 = 54).
Answer: 54 km/h
4) Two cars are 210 km apart and drive towards each other at 40 km/hr and 50 km/hr. How long until they meet? Give answer in hours and minutes.
Solution:
Relative speed (= 40 + 50 = 90) km/hr.
Time = 210/90 = 21/9 = 7/ 3 hours.
Compute 7/3 = 2 hours +1/3 hour. (1/3 hour = 1/3 x 60 = 20) minutes
Answer: 2 hours 20 minutes
5) Two cars moving in the same direction: faster car 60 km/hr is behind a slower car 40 km/hr and is 20 km behind. How long before faster car catches up?
Solution:
Relative speed (= 60 – 40 = 20) km/hr.
Time = 20 km/ 20 km/hr = 1 hour.
Answer: 1 hour
Medium
6) A car travels 100 km at 50 km/hr and another 100 km at 75 km/hr. Find the average speed for the whole trip. (Equal distances)
Solution:
For equal distances use harmonic mean: Avg = 2v_1v_2/ (v_1+v_2) = 2 x 50x 75/ (50+75).
Compute numerator: (2 x50 = 100); (100 x75 = 7500). Denominator (=125). Then (7500/ 125
Compute (125 x 60 = 7500). So average = 60 km/hr.
Answer: 60 km/hr
7) A vehicle runs 2 hours at 60 km/hr and 3 hours at 80 km/hr. What is its average speed? (Equal times? no — different times)
Solution:
Total distance = 60 x 2 + 80 x 3 .
Compute: (60 x 2=120). (80 x 3=240).
Sum =120+240=360 km.
Total time = 2+3 = 5 hours.
Average speed (= 360 / 5 = 72) km/hr.
Answer: 72 km/hr
8) A train 240 m long passes a platform 360 m long in 36 seconds. Find the speed of the train in km/hr.
Solution:
Distance to cover (= 240 + 360 = 600) m. Time = 36 s. Speed (m/s) (=600 / 36).
Compute (600 / 36): divide both by 12 → (50 / 3 = 16x 2/3 m/s (or (50/3)).
Numerically (50 / 3 = 16.666…
Convert to km/hr: multiply by (18/5): 50 / 3 x 18/5 = 50 x 18 / 3 x 5} = 900/ 15 = 60).
Answer: 60 km/hr
9) Two trains A (200 m) and B (150 m) move in the same direction with speeds 72 km/hr and 54 km/hr respectively. How long will A take to completely overtake B if A is behind? Give answer in seconds.
Solution:
Convert speeds to m/s: 72 x 5/18
Compute 72 / 18=4, (4×5=20) → 20 m/s.
For 54 km/hr: (54/18=3), (3×5=15) → 15 m/s.
Relative speed (= 20 – 15 = 5) m/s.
Distance to cover (for complete overtake) = (200 + 150 = 350) m.
Time (= 350 / 5 = 70) seconds.
Answer: 70 seconds
10) Two trains of lengths 120 m and 180 m are moving in opposite directions with speeds 36 km/hr and 54 km/hr. How long do they take to cross each other? (seconds)
Solution:
Convert speeds: 36 km/hr → (36/18=2); (2×5=10 m/s.
54 km/hr → (54/ 18=3); (3×5=15) m/s.
Relative speed (= 10 + 15 = 25) m/s.
Distance to cover = (120 + 180 = 300) m.
Time (= 300 / 25 = 12) seconds.
Answer: 12 seconds
11) A boat rows at 15 km/hr in still water; stream speed is 3 km/hr. How long will it take to go 54 km downstream and come back 54 km upstream? (hours)
Solution:
Downstream speed (= 15 + 3 = 18) km/hr. Upstream speed (= 15 – 3 = 12) km/hr.
Time downstream (= 54 / 18 = 3) hours (since (18×3=54)).
Time upstream (= 54 / 12 = 4.5) hours (since (12 x 4.5=54)).
Total time (= 3 + 4.5 = 7.5) hours.
Answer: 7.5 hours
12) Two people start from towns X and Y, 32 km apart, and walk towards each other at 5 km/hr and 3 km/hr. When do they meet?
Solution:
Relative speed (= 5 + 3 = 8) km/hr. Time (= 32 / 8 = 4) hours.
Answer: After 4 hours
13) A walker leaves at 5 km/hr. Two hours later, a cyclist starts from same point at 15 km/hr. How long after the cyclist starts will he catch the walker?
Solution:
Lead distance (= 5 x 2 = 10) km. (Because walker had 2 hours head start.)
Relative speed (= 15 – 5 = 10) km/hr.
Time (= 10 / 10 = 1) hour.
Answer: 1 hour after cyclist starts
Hard / Exam-style
14) A man travels half the distance at 5 km/hr and the other half at 10 km/hr. What is his average speed for the whole journey?
Solution:
For equal distances, average speed (= 2v_1v_2/ (v_1+v_2). Here (v_1=5, v_2=10).
Compute numerator: (2 x 5 x 10 = 100). Denominator = (5 + 10 = 15). So avg (= 100 / 15 = 100/15} = 20/3 km/hr.
Compute decimal: (20 / 3 = 6.666….
Answer: 20/3 km/hr ≈ 6.6667 km/hr
15) A man travels 120 km: first 40 km at 30 km/hr and remaining 80 km at 60 km/hr. What is his average speed for the whole journey?
Solution:
Time for first part = 40 / 30 = 40/30 = 4/3 hours = 1.3 h.
(Compute: (40/30 = 1 remainder 10 → (1 x 10/30=1x 1/3)
Time for second part (= 80 / 60 = 80/60 = 4/3 hours = 1.3 h.
Total time = 4/3 + 4/3 = 8/3 hours = 2 x 2/3 h = 2.666.. h.
Total distance = 120 km.
Average speed = 120 / 8/3 = 120 x 3/ 8 = 360 /8.
Compute 360 / 8 = 45
Answer: 45 km/hr
16) A car runs 2 hours at 72 km/hr and then 3 hours at 54 km/hr. Find the average speed for the entire trip.
Solution:
Distance1 = 72x 2 = 144 km. (Since (72x 2=144).)
Distance2 = 54x 3 = 162 km. (Since (54 x 3=162).)
Total distance (= 144 + 162 = 306) km. Total time = (2 + 3 = 5) hours.
Average speed (= 306 / 5 = 61.2) km/hr.
(Compute (5 x 61=305), remainder 1 → (61.2).)
Answer: 61.2 km/hr
17) Two trains of lengths 125 m and 175 m cross each other moving in opposite directions in 10 seconds. If one train’s speed is 72 km/hr, find the speed of the other (in km/hr).
Solution:
Total distance to cover = (125 + 175 = 300) m. Time = 10 s. So relative speed (m/s) (= 300 / 10 = 30 m/s.
Convert known speed 72 km/hr to m/s: (72 / 18 = 4); (4 x 5 = 20) m/s.
Let other train speed = v_m/s. Then (20 + v_m/s = 30).
So v_m/s = 10 m/s.
Convert back to km/hr: 10 x 18/5 = 36 km/hr.
Answer: 36 km/hr
18) Train A (length 200 m) runs at 90 km/hr and train B (length 150 m) at 60 km/hr in the same direction. If A is behind B, how many seconds will A take to completely overtake B?
Solution:
Convert speeds to m/s: 90 / 18 = 5; 5 x 5 = 25 m/s. (Alternate: 90 x 5/18=25)
For 60 km/hr: (60 / 18 = 60/18 = 10/ 3; (10/3 x 5 = 50/3 approx 16.6 m/s.
(But compute exactly: 60 x 5/18 = (60 / 18) x 5 = 3.3 x 5 = 16.6
Relative speed = 25 – 50/3 = (75-50)/ 3 = 25/ 3 m/s.
Distance to cover = 200 + 150 = 350) m.
Time (= 350 / 25/3 = 350 x 3/25 = 1050/25.
Compute 1050 / 25): = 42
Answer: 42 seconds
19) A boat covers 30 km downstream in 2 hours and returns upstream the same 30 km in 3 hours. Find the speed of the boat in still water and the speed of the stream.
Solution:
Downstream speed = 30 / 2 = 15 km/hr.
Upstream speed = 30 / 3 = 10 km/hr.
Let boat speed in still water = b, stream = s. Then (b + s = 15) and (b – s = 10).
Add: (2b = 25) ⇒ (b = 12.5) km/hr.
Subtract: (2s = 5) ⇒ (s = 2.5) km/hr.
Answer: Boat = 12.5 km/hr, Stream = 2.5 km/hr
20) A train passes a signal (pole) in 30 seconds and passes a platform of length 200 m in 50 seconds. Find the length of the train and its speed in km/hr.
Solution:
Let train length = L (m), speed = v (m/s).
Passing pole: time (t_1 = 30 = L / v) ⇒ (L = 30v). ……(1)
Passing platform: time (t_2 = 50 = (L + 200) / v⇒ (L + 200 = 50v). ……(2)
Subtract (1) from (2): ((L+200) – L = 50v – 30v == 200 = 20v). So (v = 200 / 20 = 10) m/s.
Now (L = 30v = 30x 10 = 300 m.
Convert speed to km/hr: (10 x 18/ 5 = 10 x 3.6 = 36) km/hr.
Answer: Train length = 300 m; Speed = 36 km/hr
