Speed Time & Distance for SSC SBI RRB EXAMS

Speed

Time &

Distance

🚀 Basic Formulas

Speed = Distance / Time

Speed (km/hr or m/s) = Distance / Time 

Distance = Speed × Time
Time = Distance / Speed

🔄 Unit Conversions

1 km/hr = (5/18) m/s
1 m/s = (18/5) km/hr

🔁 Use this when the question has mixed units.

🧠 Average Speed

Average Speed (when distance is same):

Average Speed = (2xy) / (x+y)

Where x and y are speeds in two legs of the journey.

Average Speed (different distances):

= Total Distance / Total Time

🏃‍♂️ Relative Speed

Same Direction:

Relative Speed = Speed1 − Speed2

Opposite Direction:

Relative Speed = Speed1 + Speed2

🚂 Train-Related Formulas

Time taken by train to cross a pole or standing object:

Time = Length of Train / Speed

Time taken to cross a platform or another train:

Time = Total Length / Relative Speed 

Total Length = Length of Train + Length of Platform/Train

💡 Boat and Stream

Speed of Boat in Still Water (B), Speed of Stream (S):
1. Downstream speed = B + S
1. Upstream speed = B – S

Speed of Boat in Still Water:

( Downstream Speed + Upstream Speed ) / 2

Speed of Stream:

( Downstream Speed – Upstream Speed ) / 2

🧍‍♂️💨 Meeting and Overtaking

Meeting Point:

Time = Distance between them / Relative Speed

If A overtakes B:

Time = Distance Relative / Speed 

If you want shortcut tricks, concept notes, or PDF revision sheets, let me know , join telegram channel & subscribe youtube channel also — I can create them tailored for SSC/Bank/RRB-type questions.

Sajesh covers two distances — 10 km in 1 hour and 20 km in 5 hours. What is Rajesh’s average speed for the entire journey?

a) 4 km/h

b) 5 km/h

c) 6 km/h

d) 7 km/h

Q2.

Parth travels 18 km in 12 minutes. If his speed decreases by 30 km/h, how much time will he take to cover the same distance?

Options:
a) 16 minutes
b) 17 minutes
c) 18 minutes
d) 19 minutes
e) None of these

Q3.

A man walks to his office at 7/9 of his usual speed and reaches 10 minutes late. Find his usual time (in minutes).

Options:
a) 30 minutes
b) 32 minutes
c) 34 minutes
d) 35 minutes
e) None of these

Q4.

A man walks at 12 km/h and takes 4 minutes rest after every 1 km. Find the total time (in minutes) required to cover 8 km.

Options:
a) 66 minutes
b) 67 minutes
c) 68 minutes
d) 69 minutes
e) None of these

Q5.

Priya runs at 8 km/h and takes a 5-minute rest after every 3 km. Find the total time (in minutes) to cover 56 km.

Options:
a) 530 minutes
b) 525 minutes
c) 510 minutes
d) 515 minutes
e) None of these

Q6.

A car runs at 7/8 of its usual speed and reaches the destination 20 minutes late. What is the usual time (in minutes) it takes to complete the journey?

Options:
a) 140 minutes
b) 150 minutes
c) 160 minutes
d) 170 minutes
e) None of these

Q7.

A student, while cycling to the city library, slows down to 3/4th of his normal speed and ends up arriving 20 minutes late. What is the actual time he takes to reach the library at his normal speed?

Options:
a) 80 minutes
b) 60 minutes
c) 70 minutes
d) 50 minutes
e) 45 minutes

Q8.

Priya cycles to her workplace at 20 km/h and arrives 13 minutes late. If she cycles faster by 10 km/h, she reaches 7 minutes early. Find the distance between her home and workplace.

Options:
a) 18 km
b) 20 km
c) 22 km
d) 24 km
e) None of these

Q9.

An athlete runs from stadium A to stadium B, to cover a distance of 72 km. He runs at x km/h and arrives 1.2 hours late. When he increases his speed by 16 km/h, he reaches exactly on time. What is his actual running speed?

Options:
a) 36 km/h
b) 38 km/h
c) 40 km/h
d) 24 km/h
e) None of these

Q10.

Mehul drives from his home to his workplace at 30 km/h and arrives 18 minutes late. If he increases his speed by 6 km/h, he reaches on time. Find the distance between his home and workplace.

Options:
a) 18 km
b) 27 km
c) 36 km
d) 45 km
e) None of these

1) Solution

Total distance = 10 + 20 = 30 km

Total time = 1 + 5 = 6 hours

Average speed = 30 ÷ 6 = 5 km/h

2) Solution

Original speed = 18 ÷ (12/60) = 90 km/h

New speed = 90 – 30 = 60 km/h

Time = 18 ÷ 60 = 0.3 hours = 18 minutes

3) Solution

Let usual time = T minutes

New time = (9/7) × T

Delay = New time – Usual time = (9/7)T – T = (2/7)T = 10

T = (10 × 7) / 2 = 35 minutes

P a g e | 45

Speed, Time & Distance

4) Solution

Time to walk 1 km = 60 / 12 = 5 minutes

Total walking time for 8 km = 8 × 5 = 40 minutes

Number of rests = 7 (after every km except the last)

Total resting time = 7 × 4 = 28 minutes

Total time = 40 + 28 = 68 minutes

5) Solution

Time to run 1 km = 60 / 8 mins

Total running time = 56 × 60/ 8 = 420 minutes

Number of rests = (56 / 3) – 1 = 18 (since rest after every 3 km except at the

end)

Total resting time = 18 × 5 = 90 minutes

Total time = 420 + 90 = 510 minutes

6) Solution

Let usual time = x hours

Reduced speed = 7x/8

New time = x × 8/7 → Delay = (8x/7 − x) = x/7

Given x/7 = 20/60 = 1/3

x = 1/3 × 7 = 7/3 = 2 hours 20 minutes

7) Solution

Let actual speed = 4x, reduced speed = 3x

Let actual time = t hours

Then distance = 4x × t = 3x × (t + 1/3)

→ 4t = 3(t + 1/3)

→ 4t = 3t + 1

→ t = 1 hour = 60 minutes

8) Solution

Let the distance = D km

Let the usual time = T hours

Using time = distance/speed:

At 20 km/h, time taken = T + 13/60

At 30 km/h, time taken = T – 7/60

Distance is same, so:

20(T + 13/60) = 30(T – 7/60)

47 / 60 = 10T ,

Distance D = 20 × (T + 13/60) = (47 / 60 + 13 / 60) *20

20km.

9) Solution

Let actual speed = S km/h , Time taken at speed S = T hours (on time)

Given distance = 72 km , At speed (S – 16), he is late by 1.2 hours:

Time taken = T + 1.2 = 72 / (S – 16)

Time on time = T = 72 / S

So,

72 / (S – 16) = 72 / S + 1.2

Multiply both sides by S(S -16):

72S = 72(S – 16) + 1.2 S (S -16)

72S = 72S – 1152 + 1.2 S² – 19.2 S

0 = -1152 + 1.2 S² – 19.2 S

1.2 S² – 19.2 S – 1152 = 0

Divide entire equation by 1.2:

S² – 16 S – 960 = 0

Solve quadratic:

S = [16 ± √(16² + 4×960)] / 2

= [16 ± √(256 + 3840)] / 2

= [16 ± √4096] / 2

= [16 ± 64] / 2

Take positive root:

S = (16 + 64)/2 = 80/2 = 40 km/h

Answer: 40 km/h

10 solution

ratio of speed 30:36 = 5:6

One unit different = 18 min

At 30km/h speed time is 1.8 hours, distance = 30*1.8 = 54km

Q11.

Sunil cycles from City A to City B covering 240 km in 6 hours. He returns from B to A at a speed 50% faster than his onward speed. What is his average speed for the entire journey?
a) 44 km/h
b) 46 km/h
c) 48 km/h
d) 50 km/h
e) None of these

Q12.

Neha drives from City X to City Y in 6 hours and takes 2 hour more to return. The total distance covered in both trips is 720 km. What is her approximate average speed for the entire journey?
a) 35 km/h
b) 36 km/h
c) 37 km/h
d) 38 km/h
e) 40 km/h

Q13.

A train travels at 54 km/h and takes 7.5 hours to complete its journey. If a bus moves at 75% of the train’s speed, how much time will the bus take to cover 80% of the train’s distance?
a) 7 hours
b) 7.5 hours
c) 8 hours
d) 8.5 hours
e) None of these

Q14.

A delivery van covers 180 km in 5 hours. If a bikeman travels at a speed 12 km/h less than twice the speed of the van, how long will the bike take to cover a distance that is 75% more than the van’s distance?

a) 6 hours
b) 7.5 hours
c) 5.25 hours
d) 3.5 hours
e) None of these

Q15.

Sneha jogs from her home to the park, a distance of 54 km, in 4.5 hours. On the return journey, she slows down to 80% of her original jogging speed. How long will she take to jog 24 km at this slower speed?
a) 2 hours
b) 2.5 hours
c) 3 hours
d) 3.2 hours
e) None of these

Q16.

A cyclist covers half of a total distance at a speed of 50 km/h and the remaining half at 6/5 of that speed. If the total time taken is 6.6 hours, find the total distance travelled.
a) 350 km
b) 360 km
c) 370 km
d) 380 km
e) None of these

Q17.

A runner completes 270 km in 9 hours. A cyclist’s speed is 10% less than the runner’s speed, and a motorcyclist’s speed is 20% more than the runner’s speed. What is the difference in time taken by the cyclist and the motorcyclist to cover 270 km?
a) 2 hours
b) 2.5 hours
c) 3 hours
d) 3.5 hours
e) None of these

Q18.

A bus A travels a distance at 40 km/h in 5 hours, while another bus B covers the same distance in 8 hours. If bus A travels 245 km at the bus B’s speed and bus B travels 280 km at the bus A’ s speed, find the total time taken by both.

16 hours b) 16.5 hours c) 16.8 hours d) 17 hours e) None of these

19)

A cat starts running and after 20 seconds, a dog notices it and begins chasing at 20 m/s. The dog catches the cat in 20 seconds. Find 13/25th of the cat ’s speed.

4.8 m/s b) 5.0 m/s c) 5.2 m/s d) 5.4 m/s e) None of these

Q20.

A deer runs at 25 m/s. The distance between the deer and a cheetah is 0.5 km. The cheetah starts chasing the deer at a speed 80% faster than the deer. How long will the cheetah take to catch the deer?
a) 18 seconds
b) 30 seconds
c) 40 seconds
d) 25 seconds
e) 20 seconds

Q21.

A tourist bus covers 150 km in 3 hours. Then it continues for another 2 hours at a steady speed of 60 km/h. What is the bus’s average speed over the whole journey?
a) 55 km/h
b) 58 km/h
c) 60 km/h
d) 62 km/h
e) None of these

Q22.

Every day, Sameer cycles to the sports complex at a speed of 60 km/h and returns home at a faster speed of 90 km/h. What is his average speed for the entire round trip?
a) 70 km/h
b) 72 km/h
c) 75 km/h
d) 78 km/h
e) None of these

Q23.

A boy covers a total distance of 1.44 km. He walks the first one-third of the journey at 2 m/s and rides a bicycle for the remaining distance at 12 m/s. What is his average speed for the entire trip?
a) 4 m/s
b) 4.2 m/s
c) 4.5 m/s
d) 5 m/s
e) None of these

Q24.

A car travels at 18 m/s for one-third of the total journey time. Then it moves at 25 m/s for 60% (or 3/5) of the remaining time. For the rest of the time, it travels at speed V. If the average speed of the car is 24 m/s, find V in km/h.
a) 96 km/h
b) 10 2 km/h
c) 108 km/h
d) 114 km/h
e) None of these

Q25.

A man rides his bike at 72 km/h. After every 20 minutes of riding, he takes a 3-minute break. How far will he travel in 100 minutes?

a) 100.8 km

b) 103.2 km

c) 105.6 km

d) 108 km

e) None of these

Q26.

Rahul drove from Agra to Jaipur at 60 km/h for the first half of the journey. For the second half, he reduced his speed by 20 km/h. What was Rahul’s average speed for the entire journey?

a) 46 km/h
b) 48 km/h
c) 50 km/h
d) 52 km/h
e) None of these

Q27.

A man travels a certain distance at 8 km/h and reaches 12 minutes late. If he increases his speed to 12 km/h, he is late by only 2 minutes. What is the exact time he should take to reach on time (without any delay)?

a) 15 minutes
b) 18 minutes
c) 20 minutes
d) 22 minutes
e) None of these

Q28.

Karan travelled from City X to Y at 40 km/h and then from Y to Z at 60 km/h. If his average speed for the entire journey is 52 km/h, what is the ratio of the distances XY to YZ?
a) 3 : 7
b) 4 : 9
c) 5 : 8
d) 7 : 9
e) None of these

Q29.

The distance between Pune and Mumbai is 324 km. Two bikes start simultaneously from Pune and Mumbai towards each other and meet after 4 hours. One bike travels 9 km/h faster than the other. What is the speed of the slower bike?
a) 34 km/h
b) 35 km/h
c) 36 km/h
d) 37 km/h
e) None of these

Q30.

Meera travels 240 km by car at a speed of 4k km/h and then 360 km by train at 6k km/h. If the total journey takes 8 hours, find the value of 5k.
a) 65
b) 70
c) 75
d) 80
e) None of these

Q31.

A runner covers 720 km in 12 hours. The ratio of the speed of a sprinter to the runner is 4:5, and the ratio of the speed of a cyclist to the sprinter is 7:6. How far will the cyclist travel in 5 hours 30 minutes?

Q32.

Soham drives his car on a weekend trip. He covers the first 200 km at a speed of 40 km/h and then continues for another 250 km at a speed of 50 km/h. What is his average speed for the entire journey?
a) 55 km/h
b) 45 km/h
c) 42 km/h
d) 38 km/h
e) None of these

Q33.

A driver covers a certain route at x km/h in 10 hours. If he slows down by 20 km/h, he takes 2 hours more to complete the journey. Find the value of x.
a) 105
b) 90
c) 120
d) 100
e) None of these

Q34.

A car travels a certain distance. When its speed increases from 144 km/h to 180 km/h, it saves 1 hour 20 minutes. Find the total distance covered by the car.
a) 900 km
b) 920 km
c) 960 km
d) 950 km
e) None of these

Q35.

Two runners start from points M and N towards each other at the same time. They meet after 2 2/9 hours. The distance between M and N is 400 km. If runner A’s speed is 20 km/h more than runner B’s speed, find the speed of runner B.
a) 75 km/h
b) 78 km/h
c) 80 km/h
d) 85 km/h
e) None of these

Q36.

Ravi cycles to his friend’s house, which is 24 km away. If he cycles 2 km /h faster, he saves 1 hour. If he cycles 2 km/h slower, he takes 2 hours more than his usual time. What is his usual time to reach his friend’s house?
a) 3 hours
b) 4 hours
c) 5 hours
d) 6 hours
e) None of these

Q37.

Neha is traveling to a mountain resort 400 km away from her home. If she covers 160 km by scooter and the remaining distance by bicycle, she reaches in 11 hours. However, if she travels 80 km by bicycle and the remaining distance by scooter, she takes 12 hours. What is the speed of the scooter?
a) 28 km/h
b) 30 km/h
c) 32 km/h
d) 34 km/h
e) None of these

Q38.

A cyclist and a jogger start at the same time. The cyclist takes the same time to cover D km as the jogger takes to cover (D + 80) km. The speed ratio of cyclist to jogger is 3:4. If the cyclist covers (D + 60) km in 5 hours, what is the jogger’s speed?

a) 70 km/h
b) 75 km/h
c) 80 km/h
d) 85 km/h
e) None of these

Q39.

Two hikers, Riya and Sameer, start from the same point and walk along the same trail at different speeds. The ratio of time taken by Riya and Sameer to complete the trail is 4:5. Riya covers (x + 40) km in 6 hours, while Sameer covers 240 km in 6 hours. How long will Sameer take to walk (x + 20) km?
a) 5 hours
b) 6 hours
c) 7 hours
d) 8 hours
e) None of these

Q40.

Ranchi and Dhanbad are 400 km apart. Rajat leaves Ranchi at 5:30 a.m. on his scooter at a speed of 60 km/h. Two hours later, at 7:30 a.m., Manish starts from Dhanbad towards Ranchi at a speed of 80 km/h. At what time will Rajat and Manish meet?
a) 9:00 a.m.
b) 8:50 a.m.
c) 9:30 a.m.
d) 8:45 a.m.
e) None of these

Solutions from 11 to 40

11) Solution: Speed from A to B = 240 ÷ 6 = 40 km/h
Return speed = 40 + 50% of 40 = 40 + 20 = 60 km/h
Average speed = (2 × 40 × 60) ÷ (40 + 60) = 4800 ÷ 100 = 48 km/h

12) Solution: Total distance = 2D = 720 km ⇒ D = 280 km
Time from X to Y = 6 hr, Y to X = 7 hr
Average speed = 560 ÷ (6 + 8) = 560 ÷ 14 = 40 km/h

13) Solution: Train distance = 54 × 7.5 = 405 km
Bus speed = 75% of 54 = 75/100*(54) km/h
Bus distance = 80% of 405 =
Time = (.8(54*7.5) km ) / .75*(54) km/h = 8 hr

14) Solution: Van speed = 180 ÷ 5 = 36 km/h
Bike speed = 2 × 36 − 12 = 60 km/h
Bike distance = 180 + 135 = 315 km
Time = 315 ÷ 60 = 5.25 hr

15) Solution: Original speed = 54 ÷ 4.5 = 12 km/h
Reduced speed = 80% of 12 = 9.6 km/h
Time = 24 ÷ 9.6 = 2.5 hr

16) Solution: Let distance = D
Time = (D)÷50 + (D÷2)÷60 = 6.6
D/100 + D/120 = 6.6 ⇒ (22D) ÷ 1200 = 6.6 ⇒ D = 360 km

17) Solution: Runner speed = 270 ÷ 9 = 30 km/h
Cyclist speed = 0.9 × 30 = 27 km/h
Motorcyclist speed = 1.2 × 30 = 36 km/h
Time diff = 270 ÷ 27 − 270 ÷ 36 = 10 − 7.5 = 2.5 hr

18) Solution: bus A speed = 40 km/h, bus B speed = 25 km/h
Bus A at partner speed = 245 ÷ 25 = 9.8 hr
Bus B at courier speed = 280 ÷ 40 = 7 hr
Sum = 9.8 + 7 = 16.8 hr

19) Solution: Time before and during chase = 20 + 20 = 40 sec cat
Distance = 20 × 20 = 400 m
cat speed = 400 ÷ 40 = 10 m/s
Required = (13/25) × 10 = 5.2 m/s

20) Solution: Distance = 0.5 km = 500 m
Deer speed = 25 m/s, Cheetah = 25 + 0.8 × 25 = 45 m/s
Relative speed = 20 m/s
Time = 500 ÷ 20 = 25 sec

21) Solution: First part: 150 km in 3 hr, Second: 120 km in 2 hr
Avg speed = (150 + 120) ÷ 5 = 54 km/h

22) Solution: Avg speed = (2 × 60 × 90) ÷ (60 + 90) = 10800 ÷ 150 = 72 km/h

23) Solution: Total = 1440 m. Walk = 480 m, Bike = 960 m
Time = 480/2 + 960/12 = 240 + 80 = 320 sec
Avg speed = 1440 ÷ 320 = 4.5 m/s

24) Solution: (18 × 1/3) + (25 × 2/5) + (V × 4/15) = 24
6 + 10 + 4V/15 = 24 ⇒ 4V = 120 ⇒ V = 30 m/s = 108 km/h

25) Solution: One bike ride = 23 min, bike one cycle time in 100 min = 4 (92 min)
Remaining = 8 min, Total ride = 88 min = 22/15 hr
Distance = 72 × 22/15 = 105.6 km

26) Solution: Time = D/60 + D/40 = (5D) ÷ 120 = D/24
Avg speed = 2D ÷ (D/24) = 48 km/h

27) Solution: Distance = 8(T + 1/5) = 12(T + 1/30)
Solve: T = 3/10 hr = 18 min

28) Solution: Avg speed = (x + y) ÷ (x/40 + y/60) = 52
Solve: x/y = 4/9

29) Solution: (2x + 9) × 4 = 324 ⇒ 8x + 36 = 324 ⇒ x = 36 km/h

30) Solution: 240/(4k) + 360/(6k) = 8 ⇒ 120/k = 8 ⇒ k = 15
5k = 75

31) Solution: Runner = 60, Sprinter = 48, Cyclist = 56 km/h
Cyclist time = 5.5 hr ⇒ Distance = 56 × 5.5 = 308 km

32) Solution: Avg speed = (200 + 250) ÷ (5 + 5) = 45 km/h

33) Solution: 10x = (x − 20)(12) ⇒ x = 120 km/h

34) Solution: Time saved = 4/3
Solve: d = 960 km

35) Solution: Let speed of runner B = x km/h

Speed of runner A = x + 20 km/h

Time = 2 2/9 = 20/9 hours

(20x/9) + (20x + 400)/9 = 400 ⇒ x = 80

36) Solution: From equations, x = 6 km/h ⇒ Time = 24 ÷ 6 = 4 hr

37) Solution: y = 40, x = 32 ⇒ Scooter speed = 32 km/h

38) Solution: D = 240 ⇒ Cy clist speed = 60 km/h ⇒ Jogger = 80 km/h

39) Solution: ((x + 40)/6)/40 = 5/4 ⇒ x = 260
Distance = 280, Speed = 40 ⇒ Time = 7 hr

40) Solution: Distance left = 280 km, Relative speed = 140 km/h
Time = 280 ÷ 140 = 2 hr ⇒ Meeting time = 9:30 a.m.

Q41.

Two friends, Neeraj and Tarun, start cycling towards each other from towns 96 km apart. They meet after 8 hours. If Neeraj had reduced his speed to 3/4 and Tarun increased his speed to 5/2 of their original speeds, they would have met in 6 hours. What is Neeraj’s actual speed in km/h?
a) 4
b) 6
c) 8
d) 10
e) None of these

Q42.

Suman and Harish start driving from the same location at the same time in the same direction. Suman drives at a constant speed of 10 km/h, while Harish starts at 8 km/h but increases his speed by 0.5 km/h every hour. Assuming both drive continuously without stopping, after how many hours will Harish catch up with Suman?
a) 4 hours
b) 5 hours
c) 6 hours
d) 8 hours
e) None of these

Q43.

An ambulance driver notices a bus 40 meters ahead. After 20 seconds, the ambulance has passed the bus and is now 60 meters ahead. If the ambulance is moving at 30 km/h, what is the speed of the bus in km/h?
a) 20
b) 24
c) 25
d) 28
e) None of these

Q44.

A bus takes 6 hours to travel from city X to city Y. After covering 240 km, its speed decreases by 10%, causing the total journey to take 30 minutes longer. What is the distance between city X and city Y?
a) 900 km
b) 940 km
c) 960 km
d) 980 km
e) None of these

Q45.

Two cars start simultaneously. The faster one travels at 120 km/h, while the slower one travels at 55 km/h but must stop for 1 minute to pay toll every 27.5 km. When the faster car has covered 620 km, how far has the slower car traveled?
a) 275 km
b) 245 km
c) 255 km
d) 285 km
e) None of these

Q46.

An engine runs at 24 km/h with no wagons. Speed decreases in proportion to the square root of the number of wagons attached. When 4 wagons are attached, the speed drops to 20 km/h. What is the maximum number of wagons the engine can pull before it stops moving?
a) 145
b) 144
c) 143
d) 142
e) None of these

Q47.

A man travels from his home to his office. At 30 km/h, he arrives 10 minutes late. At 24 km/h, he is 15 minutes late. What is the distance between his home and office?
a) 10 km
b) 20 km
c) 8 km
d) 40 km
e) None of these

Q48.

A traveler covers a total distance of 82 km in 10 hours to reach a remote lakeside camp. He treks part of the journey through forest paths at 7 km/h and rows the remaining distance across a lake at 11 km/h. What distance did he cover on foot?
a) 41 km
b) 36 km
c) 35 km
d) 38 km
e) None of these

Q49.

A drone is programmed to deliver a package across a 200 km route. If its speed is reduced by 10 km/h due to strong winds, it takes 10 hours longer to complete the delivery. What was the time taken by the drone to complete the journey at its original speed?
a) 2 hours
b) 4 hours
c) 5 hours
d) 8 hours
e) None of these

50)

A passenger train leaves the station to reach a nearby town. If it moves at 60 km/h, it arrives 3 hours early. If it runs at 40 km/h, it still reaches 2 hours ahead of schedule. What is the actual speed of the train, the scheduled travel time, and the distance between the station and the town?

a) 24 km/h, 5 hr, 120 km
b) 30 km/h, 6 hr, 180 km
c) 25 km/h, 6 hr, 150 km
d) 34 km/h, 5 hr, 170 km
e) None of these

51)

A security drone detects an intruder 400 meters away and immediately begins pursuit. The drone travels at 15 km/h while the intruder moves at 10 km/h. What distance does the intruder cover before being intercepted?

a) 0.2 km
b) 0.25 km
c) 0.8 km
d) 1.5 km
e) 1.2 km

52)

An intruder is detected 400 meters ahead by a patrolling robot and begins to flee. The intruder can cover 2 km in 12 minutes, while the robot can cover 3 km in 10 minutes. How far does the intruder manage to run before the robot catches up?

a) 400 meters
b) 500 meters
c) 600 meters
d) 460 meters
e) 480 meters

53)

Two courier vans—one from Agra and the other from Kanpur—start moving toward each other at the same time. Both begin at a speed of 10 km/h. After 2 hours, the van from Agra increases its speed by 2 km/h, while the one from Kanpur reduces its speed by 2 km/h. The distance between Agra and Kanpur is 120 km. After how many total hours do the vans meet?

a) 5 hours
b) 4 hours
c) 6 hours
d) 8 hours
e) 3 hours

54)

A delivery robot departs from the warehouse to a distant hub. For the first 5 hours, it moves steadily at 5 km/h. Over the next 5 hours, it accelerates by 5 km/h every hour. Then, during the final 5 hours, it slows down at the same rate—by 5 km/h per hour. What is the total distance between the warehouse and the delivery hub?

a) 200 km
b) 250 km
c) 275 km
d) 225 km
e) None of these

55)

A delivery worker travels from his apartment to the dispatch center using a scooter and returns home by walking. The total round-trip takes him 4 hours. However, if he walks both ways, it takes him 6 hours. If the one-way distance between his apartment and the dispatch center is 48 km, what was his speed while riding the scooter?

a) 36 km/hr
b) 24 km/hr
c) 16 km/hr
d) 96 km/hr
e) 48 km/hr

56)

Two cyclists, Rahul and Sneha, start riding toward each other from two distant checkpoints on a long forest trail. Rahul pedals from Checkpoint A at a speed of 45 km/h, and Sneha starts from Checkpoint B at the same time. After meeting each other on the trail, Rahul takes 4 hours to reach Checkpoint B, and Sneha takes 9 hours to reach Checkpoint A. What was the total length of the trail and what was Sneha’s speed?

a) 450 km, 30 km/hr
b) 450 km, 20 km/hr
c) 360 km, 20 km/hr
d) 360 km, 30 km/hr
e) None of the above

57)

An adventure trekker begins a journey from Base Camp A to Camp B, covering a distance of 160 km across rocky terrain at an average speed of 40 km/hr. From Camp B to Summit Point C, he covers 360 km across icy slopes at a speed of X km/hr. The average speed for the entire journey from A to C is 52 km/hr. Find the value of X.

a) 55 km/hr
b) 60 km/hr
c) 50 km/hr
d) 35 km/hr
e) None of these

58)

An intercity express train normally runs at a speed of 60 km/hr between Station A and Station B. On one occasion, the train increased its speed by 10 km/hr and managed to reduce the travel time by 50 minutes. What is the distance between Station A and Station B?

a) 420 km
b) 350 km
c) 300 km
d) 320 km
e) None of these

59)

Two research teams start walking toward each other from two remote campuses. Team A starts from Campus Alpha at 1:00 AM and reaches Campus Beta at 3:00 PM. Meanwhile, Team B departs from Campus Beta at 1:00 AM and arrives at Campus Alpha at 1:00 PM. Assuming both teams travel at a constant pace along the same straight path, approximately at what time will the two teams meet?

a) 8:35 AM
b) 6:55 AM
c) 7:28 AM
d) 8:05 AM
e) None of these

60)

A wildlife researcher travels from Base Camp X to Observation Point Y, which are 600 km apart, riding an off-road bike at a speed of 50 km/hr. After covering two-thirds of the journey, he halts for a 2-hour break. To reach the observation point on time (as per his original plan), he increases his speed for the remaining journey. The increased speed is what percentage of his original speed?

a) 125%
b) 150%
c) 160%
d) 175%
e) 200%

61)
Priya starts driving from City M towards City N at 9:00 am at a constant speed of 50 km/hr. At 11:00 am, her friend Neha starts from City N towards City M at a speed of 60 km/hr. The distance between the two cities is 1200 km. What is the total distance covered by Priya by the time she crosses Neha on the way?

a) 500 km
b) 540 km
c) 600 km
d) 700 km
e) None of these

62)
Two friends, Rahul and Sameer, decided to walk the same distance along a countryside trail. Rahul walks at a speed of 8 km/hr, while Sameer walks at a slower speed of 6 km/hr. If Sameer takes 1 hour 40 minutes more than Rahul to finish the distance, what is the total length of the trail?

a) 35 km
b) 48 km
c) 42 km
d) 40 km
e) None of these

63)
Rohit went on a one-hour road trip using his scooter. While the scooter’s speed is normally 60 km/hr, due to short halts at traffic signals and snack breaks, his effective average speed dropped to 48 km/hr. For how many minutes did he stop during his trip?

a) 12 minutes
b) 15 minutes
c) 18 minutes
d) 5 minutes
e) None of these

64)
On the school playground, two children—Riyaz and Mohit—are playing a game of tag. Mohit starts running ahead of Riyaz and maintains a 450-meter lead. Riyaz chases Mohit at a speed of 18 meters per second, while Mohit runs at 9 meters per second. What is the total distance Riyaz runs before catching Mohit?

a) 850 m
b) 810 m
c) 720 m
d) 900 m
e) None of these

65)
Two cyclists, Ayaan and Kabir, are riding on a racing track in the same direction. Ayaan rides at a speed that is 2.4 times faster than Kabir. The length of Kabir’s bicycle (including him) is three times the length of Ayaan’s bicycle (including him). Kabir crosses a checkpoint (like a light pole) in 6 seconds. How much time will Ayaan take to completely overtake Kabir?

a) 4 5/7 sec
b) 5 5/7 sec
c) 5 2/3 sec
d) 4 8/9 sec
e) None of these

66)
Two cyclists, Aditya and Ramesh, start riding from two towns that are 3 hours apart from each other, moving toward one another on a long straight highway. Aditya rides at a speed of 75 km/hr from Town A, while Ramesh rides at 57 km/hr from Town B. They meet exactly after 3 hours. What is the total distance between Town A and Town B?

a) 363 km
b) 361 km
c) 384 km
d) 396 km
e) None of these

67)
Two towns, A and B, are 60 km apart. Two friends, Rohan and Sameer, start from Town A toward Town B. Rohan walks at a speed of 10 km/hr, and Sameer walks at 5 km/hr. Rohan reaches Town B and immediately turns back toward Town A. He meets Sameer at a point Y on the way. What is the distance between Town A and point Y where they meet?

a) 40 km
b) 50 km
c) 45 km
d) 53 km
e) None of these

68)
Ashwin has to walk from his home to a nearby event venue and reach there exactly on time. If he walks at a speed of 6 km/hr, he arrives 40 minutes late, but if he walks at a speed of 8 km/hr, he arrives 12 minutes early. What is the approximate distance between his home and the event venue?

a) 21 km
b) 25 km
c) 18 km
d) 32 km
e) None of these

69)
Priya rides her scooter for a total distance of 376 km in 8 hours while touring the coastal highway. Her brother, Aryan, plans to travel 14 km more than Priya on the same route but at a speed that is 18 km/hr faster than Priya’s average speed. How long will Aryan take to complete his journey?

a) 7 hr
b) 6 hr
c) 8 hr
d) 9 hr
e) None of these

70)
Two delivery agents, Arjun and Bhavesh, operate on a straight route from Hub P to Hub Q. Their delivery speeds are in the ratio 9:3. Arjun starts first from Hub P towards Q. The moment he reaches the midpoint of the route, Bhavesh begins his journey from P towards Q. Arjun reaches Hub Q, immediately turns back, and eventually meets Bhavesh at a point that is 155 meters away from Hub Q. What is the total length of the route from Hub P to Hub Q?

a) 248 m
b) 226 m
c) 328 m
d) 420 m
e) None of these

Solutions 41 to 70

41)
A + B’s speed = 12
(3/4)A + (5/2)B = 16 → 3A + 10B = 64
Solve: A = 8 km/h

42)
Suman: 10t, Harish: AP(8, 8.5, …)
Set distances equal → solve quadratic → t = 9 hours

43)
Relative distance = 100 m, time = 20s → speed = 5 m/s
Ambulance = 25/3 m/s → Bus = 10/3 m/s = 12 km/h

44)
Speed ratio = 10:9 → time diff = 0.5 hr
1.5 hr → 240 km ⇒ Speed = 160 km/h → Total = 960 km

45)
Faster car = 620/120 = 310 min
Slower car = 27.5 km in 31 min → in 310 min = 275 km

46)
Speed drop = 4 = k√4 → k = 2
Max speed drop = 24 = 2√w → w = 144 → Max = 143 wagons

47)
Speed ratio = 5:4 → time ratio = 4:5 → delay = 20 min
Distance = 30 × 1/3 = 10 km

48)
x/7 + (82−x)/11 = 10 → Solve: x = 49 km

49)
(200 / (x−10)) − (200 / x) = 10 → Solve: x = 20 km/h

50)
60(t−3) = 40(t−2) → t = 5 hr
Distance = 120 km, Speed = 24 km/h

51)
400 m = 0.4 km, Relative speed = 5 km/h
Time = 0.4/5 → Intruder = 10 × 0.08 = 0.8 km

52)
Intruder: 10, Robot: 18, Relative = 8
Time = 1/20 hr → Distance = 10 × 1/20 = 0.5 km

53)
First 2 hr = 40 km, remaining = 80 km
Relative speed = 20 → Time = 4 hr
Total = 6 hours

54)
First 5 hr = 25, next = 100, last = 75
Total = 200 km

55)
Walking both = 6 hr → W = 16 km/h
Scooter + walk = 4 hr → M = 48 km/h

56)
Ratio: 45/s = √(9/4) → s = 30
Distance = 45×4 + 30×9 = 450 km

57)
Time = 520 / 52 = 10 hr
160/40 = 4 hr → Rest = 6 hr → 360/x = 6 → x = 60 km/h

58)
x/60 − x/70 = 5/6 → Solve: x = 350 km

59)
1/(1/14 + 1/12) = 168/26 = 6 hr 28 min → Time = 7:28 AM

60)
Original speed = 50, needs 200 km in 2 hr → 100 km/h
% increase = (100/50) × 100 = 200%

61)
Priya alone: 2 hr = 100 km
Remaining = 1100 km → 110 speed → 10 hr
Total Priya = 100 + 500 = 600 km

62)
x/6 − x/8 = 5/3 → Solve: x = 40 km

63)
Loss = 12 km at 60 → Time = 12/60 = 12 min

64)
Relative = 9 m/s → Time = 50 sec
Distance = 18 × 50 = 900 m

65)
Kabir: 3L = 5S × 6 → L = 10S
Ayaan vs Kabir time = 40/7 sec = 5 5/7 sec

66)
Relative speed = 132 km/h
Time = 3 hr → Distance = 396 km

67)
Rohan: 6 hr → Sameer = 30 km
x/5 = (30−x)/10 → x = 10 → Total = 30+10 = 40 km

68)
d/6 − 2/3 = d/8 + 1/5 → Solve: d = 21 km

69)
Priya = 47, Aryan = 65 → Distance = 390 km
Time = 390/65 = 6 hr

70)
Speeds = 3:1 → time = 1:3
(4 + x)/y = 3/1 and y + x + 4 = 8
Solve → PQ = 8 units → Distance = 248 m

71)
Two delivery trucks leave a logistics hub at a speed of 40 km/hr, with a time gap of 10 minutes between their departures. An inspection officer starts from the opposite direction towards the logistics hub and encounters the trucks at a gap of 8 minutes. What is the speed of the inspection officer?

a) 14 km/hr
b) 10 km/hr
c) 12 km/hr
d) 15 km/hr
e) None of these

72)
The distance between two cities, Jaynagar and Rupnagar, is 370 km. A courier van leaves from Jaynagar towards Rupnagar at 10:00 AM at a speed of 80 km/hr. A delivery truck starts from Rupnagar towards Jaynagar at 1:00 PM, moving at 50 km/hr. At what time will both vehicles meet?

a) 1:30 PM
b) 2:00 PM
c) 2:30 PM
d) 3:00 PM
e) None of these

73)
Raghav is on a documentary assignment across a wildlife reserve. He completes 20% of the total route by jeep, and then covers 50% of the remaining distance using a combination of boat and horse-cart in the ratio 5:3, respectively. The last stretch of the journey he completes on foot. If the combined distance travelled by jeep and horse-cart is 126 km, what is the total distance of Raghav’s expedition?

a) 360 km
b) 300 km
c) 400 km
d) 320 km
e) None of these

74)
Three delivery drones — Falcon, Hawk, and Swift — are tested on a 1 km delivery route. When Falcon and Hawk fly the route, Falcon finishes 10 seconds before Hawk. When Falcon races Swift, Falcon completes the full 1 km while Swift covers only 875 meters. In another test between Hawk and Swift, Hawk finishes 15 seconds ahead over the same distance. What is the ratio of time taken by Falcon and Hawk to cover 1 km?

a) 35:47
b) 37:21
c) 35:37
d) 25:36
e) None of these

75)
A premium cargo drone typically flies 1800 km between Warehouse A and Warehouse B. On a particular day, due to strong headwinds, the drone took 30 minutes longer than usual to complete the trip, and its average speed was reduced by 300 km/h. What is the normal flying time for the drone on this route under ideal conditions?

a) 2 hr
b) 1.5 hr
c) 2.5 hr
d) 3 hr
e) None of these

76)
Rahul and Meena start moving towards a meeting point at the same time from opposite directions. Rahul increases his speed by 4 km/h every 2 hours, while Meena decreases her speed by 3 km/h every hour. Rahul’s average speed for the entire trip is 28 km/h, and the ratio of distances traveled by Rahul and Meena is 8:9. If Meena’s initial speed was 42 km/h, find Rahul’s initial speed.

a) 18 km/h
b) 25 km/h
c) 33 km/h
d) 22 km/h
e) None of these

77)
A cyclist starts from point A at 9:00 am and arrives at point B at 10:00 am. Starting at 9:00 am, a motorcycle leaves point A towards B every minute. Exactly 41 motorcycles reach B by 10:00 am, all traveling at the same speed. If the cyclist had traveled at triple his speed, how many motorcycles would have reached B by the time he arrives?

a) 5
b) 4
c) 3
d) 2
e) 1

78)
Car and a bus begin their journey from the same point ‘A’ at the same time. After t hours, the bus is 60 km ahead of the car. After 5 hours, the distance between them becomes equal to the distance the bus covers in one hour. It is also known that if the car and the bus were moving towards each other, their relative speed would be 270 km/h. What is the value of t?

a) 1
b) 2
c) 3
d) 4
e) None of these

79)
A train faces two slowdowns during its journey. The first slowdown happens 200 km from the start, reducing the train’s speed to two-thirds of its original speed. The second slowdown occurs 250 km after the first one, cutting the speed down to one-third of the original speed. Due to these delays, the train arrives 9 hours late. If both slowdowns had occurred 50 km further along the route, the train would have arrived 2 hours earlier than in the actual scenario. What was the train’s original speed?

a) 90 km/h
b) 87.5 km/h
c) 88 km/h
d) 27 km/h
e) None of these

80)
Neha has to travel 300 km to her cousin’s place using a car and a bus. If she drives the car for 180 km and takes the bus for the rest, she reaches in 6 hours. But if she rides the bus for 210 km and drives the car for the remaining distance, she arrives in 5 hours 30 minutes. What is the difference between the time taken to cover the entire distance by car alone and by bus alone?

a) 1 hour 20 minutes
b) 1 hour 30 minutes
c) 1 hour 40 minutes
d) 2 hours 15 minutes
e) 1 hour 15 minutes

81)
A car travels a total distance of 185 km. It covers a part of the journey at 5 km/h and the remaining part at 10 km/h. If the car had instead travelled the portion it originally did at 5 km/h with 10 km/h, and the portion it did at 10 km/h with 5 km/h (i.e., the speeds are swapped), it would have covered 10 km less in the same total time. What is the total time taken by the car to travel 185 km, and what is its average speed during the original journey?

a) 25.5 hr, 15/2 kmph
b) 28 hr, 7 kmph
c) 27.75 hr, 20/3 kmph
d) 26 hr, 30/4 kmph
e) None of these

82)
A car travels for three consecutive hours. In the first hour, it travels at a certain speed. In the second hour, its speed becomes three times the speed of the first hour. During the third hour, the speed becomes equal to the average of the first two hours’ speeds. If the car had maintained the second hour’s speed throughout all three hours, it would have covered 150 km more than it actually did. What is the percentage reduction in time taken in this second case, compared to the original time for the same distance?

a) 16.67%
b) 12.5%
c) 25%
d) 20%
e) None of these

Q83. Two vehicles, P and Q, travel the same total distance but with different speed patterns.
Vehicle P travels 60 km at speed a km/h, then 140 km at double that speed, and finally 135 km at speed b km/h, taking 7 hours in total.
Vehicle Q travels 60 km at speed b km/h, then 140 km at speed a km/h, and the last 135 km at twice the speed a, taking 9.1 hours in total.
What is the initial speed of Vehicle P as a percentage of the initial speed of Vehicle Q?

a) 62.5%
b) 33.33%
c) 42.85%
d) 31.25%
e) 66.66%

Q84. A vehicle travels from Delhi to Kolkata passing through points A, B, and C in that sequence.
Distances: Delhi to A = 150 km, A to B = 210 km, B to C = 180 km.
The distance from point C to Kolkata is equal to the average of these three distances.
The vehicle takes 5 hours to reach point B from Delhi.
After that, due to reduced fuel, its speed drops by 25% and remains the same till Kolkata.
What is the average speed of the entire trip?

a) 64 6/7 kmph
b) 87 5/7 kmph
c) 52 3/7 kmph
d) 61 5/7 kmph
e) 45 1/7 kmph

Speed Time Distance Questions | SSC SBI RRB (Data based )

Q85. Ravi travels on a bicycle from City P. He cycles for 1.2 hours at 10 km/h, then rests for 0.8 hours, and then continues at the same speed.
Exactly 3 hours after Ravi starts, his friend Sameer leaves City P on a motorcycle at 12.5 km/h in the same direction.
Sameer catches Ravi at a point where the distance covered is the same as the distance between two points M and N.
Separately, Mohan starts from point M at 9:00 AM at 15 km/h.
Rahul starts from point N at 10:00 AM at 23 km/h towards Mohan.
What distance does Mohan cover before meeting Rahul?

a) 52.5 km
b) 42.5 km
c) 47.5 km
d) 55.5 km
e) None of these

Q86. Car A starts from point S towards point T at 8:00 AM at a speed of ______ km/h.
Car B starts from point T towards point S at 10:00 AM at 60 km/h.
The distance between S and T is 780 km.
At what time in the afternoon do the two cars meet?

I) 40 kmph, 5:00 pm
II) 30 kmph, 4:00 pm
III) 60 kmph, 5:30 pm

a) Only II
b) Only I
c) Only II and III
d) Only I and III
e) None of these

Q87. A police officer chases a thief who is 1500 meters ahead.
The officer runs at 54 km/h and the thief at ______ km/h.
When the officer catches the thief, the total distance travelled by both is ______ kilometers, and they’ve been running for ______ minutes.
Which of the following sets of values fill the blanks correctly?

I) 18 km/h, 3 km, 2.5 minutes
II) 9 km/h, 2.1 km, 2 minutes
III) 36 km/h, 7.5 km, 5 minutes

a) Only I
b) Only II
c) Only II and III
d) All are correct
e) Only I and II

Q88. Anita and Priya start walking towards each other from points X and Y.
Anita walks at 36 km/h, while Priya walks at ______ km/h.
By the time they meet, Anita has covered 0.5 km more than Priya.
The total distance between X and Y is ______ km.
Anita takes ______ seconds to complete her part of the journey.

I) 27 km/h, 3.5 km, 200 seconds
II) 18 km/h, 1.5 km, 150 seconds
III) 13.5 km/h, 1.1 km, 80 seconds

a) Only II
b) Only III
c) Only I and III
d) Only II and III
e) All I, II, and III

Q89.
Quantity I: Rohan cycles to school at 25 km/h and returns walking at 5 km/h. The total time taken for the round trip is 3 hours. What is the distance between home and school?

Quantity II: Arjun rides a motorcycle to work. At 15 km/h, he is 30 minutes late; at 20 km/h, he is 10 minutes late. What is the total distance between his home and office?