Relative Speed MCQ Quiz - Objective Question with Answer for Relative Speed - Download Free PDF
Last updated on May 26, 2025
Latest Relative Speed MCQ Objective Questions
Relative Speed Question 1:
A rocket is launched at intervals of 11.5 seconds, moving in the same direction as a train traveling at an unknown speed. The speed of sound is 330 m/s. If a person seated inside the train hears the sound of the rocket after 11 seconds, determine the speed of the train.
Answer (Detailed Solution Below)
Relative Speed Question 1 Detailed Solution
Given:
Rocket launch interval (Tlaunch) = 11.5 s
Time sound heard in train (Theard) = 11 s
Speed of sound (Vs) = 330 m/s
Formula Used:
Theard = Tlaunch × \(\dfrac{V_s}{V_s + V_t}\) (for train moving towards source)
Calculations:
11 = 11.5 × \(\dfrac{330}{330 + V_t}\)
⇒ 11 × (330 + Vt) = 11.5 × 330
⇒ 330 + Vt = \(\dfrac{11.5 \times 330}{11}\)
⇒ 330 + Vt = 30 × 11.5
⇒ 330 + Vt = 345
⇒ Vt = 345 - 330
⇒ Vt = 15 m/s
∴ The speed of the train is 15 m/s.
Relative Speed Question 2:
An employee will be late by 12 minutes to his office if he rides his bike at a speed of 40 kmph and he will be on time to his office if he rides his bike at a speed of 50 kmph. Then the distance (in km) of his office from his house is
Answer (Detailed Solution Below)
Relative Speed Question 2 Detailed Solution
Given:
At 40 kmph → late by 12 minutes
At 50 kmph → on time
Formula used:
Time difference = Distance × (1/s1 − 1/s2)
Convert 12 minutes to hours = 12 ÷ 60 = 1/5 hour
Calculation:
Let distance = d km
⇒ d × (1/40 − 1/50) = 1/5
⇒ d × (5 − 4)/200 = 1/5
⇒ d × (1/200) = 1/5
⇒ d = 200 ÷ 5 = 40
∴ The distance is 40 km.
Relative Speed Question 3:
The distance between two stations A and B is 240 km. It takes 2 hours for the two cars L and W to cross each other if they start respectively from A and B at the same time towards each other. Further, it takes 8 hours for L to overtake W if they both start at the same time from A and B in the same direction. Then the speed of the car L (in kmph) is
Answer (Detailed Solution Below)
Relative Speed Question 3 Detailed Solution
Given:
Distance between A and B = 240 km
Time to cross each other when moving toward each other = 2 hours
Time for L to overtake W when moving in same direction = 8 hours
Formula used:
When moving toward each other: (Speed of L + Speed of W) × Time = Distance
When moving in same direction: (Speed of L − Speed of W) × Time = Distance
Calculation:
Let speed of L = x km/h, speed of W = y km/h
Equation 1: (x + y) × 2 = 240 ⇒ x + y = 120
Equation 2: (x − y) × 8 = 240 ⇒ x − y = 30
Now add both equations:
x + y = 120
x − y = 30
⇒ 2x = 150 ⇒ x = 75
∴ Speed of car L is 75 km/h.
Relative Speed Question 4:
Two cars A and B travel from point P to point Q. Car A starts 1 hour before car B and reaches Q 2 hours after B when travelled at a speed 30 km/hr. If speed of car B is 50 km/hr, then find the distance between point P and point Q.
Answer (Detailed Solution Below)
Relative Speed Question 4 Detailed Solution
Calculation
We are given:
Car A starts 1 hour before Car B.
Car A reaches 2 hours after Car B.
Speed of Car A = 30 km/hr.
Speed of Car B = 50 km/hr.
Let the time taken by Car B to go from P to Q be t hours.
Then:
Car A started 1 hour earlier
→ Time taken by Car A = t + 3hours
(since it reached 2 hours after B and started 1 hour before B)
Distance = Speed × Time
Distance by Car A = 30 × (t + 3)
Distance by Car B = 50 × t
Since both travel the same distance from P to Q:
30(t+3) = 50t
Or, 30t + 90 = 50t
⇒ 90 = 20t
⇒ t = 90/20 = 4.5
Distance = 50 × 4.5 = 225 km
Relative Speed Question 5:
A thief is running away on a straight road with a speed of 8 m/s-1. A policeman chases him in a jeep moving at a speed of 10 m/s-1. If the instantaneous separation of the jeep from the motorcycle is 50 m, how long will it take for the policeman to catch the thief?
Answer (Detailed Solution Below)
Relative Speed Question 5 Detailed Solution
Given:
Speed of thief (vthief) = 8 m/s
Speed of policeman (vpoliceman) = 10 m/s
Initial separation (d) = 50 m
Formula used:
Time (t) = Distance / Relative Speed
Relative Speed = vpoliceman - vthief
Calculation:
Relative Speed = 10 - 8
⇒ Relative Speed = 2 m/s
Time (t) = 50 / 2
⇒ t = 25 s
∴ The correct answer is option (1).
Top Relative Speed MCQ Objective Questions
A, B and C run simultaneously, starting from a point, around a circular track of length 1200 m, at respective speeds of 2 m/s, 4 m/s and 6 m/s. A and B run in the same direction, while C runs in the opposite direction to the other two. After how much time will they meet for the first time?
Answer (Detailed Solution Below)
Relative Speed Question 6 Detailed Solution
Download Solution PDFGiven:
Total track length = 1200 m
Speed of A = 2 m/s ; speed of B = 4 m/s
Speed of C = 6 m/s
Formula used:
Distance = relative speed × time
Calculation:
Relative speed of A and B = (4 - 2) = 2 m/s
Relative speed of B and C = (6 + 4) = 10 m/s
Relative speed of A and C = (6 + 2) = 8 m/s
Time taken by A and B = 1200/2 = 600 sec
Time taken by B and C = 1200/10 = 120 sec
Time taken by A and C = 1200/8 = 150 sec
A, B and C will meet at = L.C.M {600,120, 150} = 600 sec = 600/60 = 10 minutes
∴ The correct answer is 10 minutes.
A thief committed a crime and escaped from the spot at a speed of 12 m/h. A Security guard started chasing him 20 minutes after the thief started running and caught him in the next 20 minutes. What is the speed (in m/h) of the Security guard?
Answer (Detailed Solution Below)
Relative Speed Question 7 Detailed Solution
Download Solution PDFConcept used:
Speed × time = distance
Calculation:
In the 1st 20 min the thief cover distance = 4 m,
20 min in hour = 20/60 hour
Let's assume that the speed of security guard = x m/hr, where x > 12
According to the question,
⇒ (x - 12) × 20/60 = 4
⇒ x - 12 = 12
⇒ x = 24
∴ The correct answer is 24 m/h
In a 900 metres race, Sathish beats Kiran by 270 metres and Rahul by 340 metres. By how many metres does Kiran beat Rahul in the same race?
Answer (Detailed Solution Below)
Relative Speed Question 8 Detailed Solution
Download Solution PDFGiven,
Sathish completes 900 m race.
Kiran covers = 900 – 270 = 630 m
Rahul covers = 900 – 340 = 560 m
⇒ Ratio of their speed = 630/560
When Kiran covers 900 m race then
⇒ Rahul would cover = 900 × 560/630 = 800 m
∴ Kiran beats Rahul by = 900 – 800 = 100 mIn a circular race of 400 m in length, A and B start at speeds of 10 m/s and 16 m/s, respectively, at the same time from the same point. After how much time will they meet for the first time at the starting point when running in the same direction?
Answer (Detailed Solution Below)
Relative Speed Question 9 Detailed Solution
Download Solution PDFGiven:
A and B start running on a circular track (length 400 m) from the same point simultaneously with speeds of 10 m/s and 16 m/s
Formula used:
Time = \(\dfrac{distance}{speed}\)
Calculations:
A takes time to complete one round = 400/10 = 40 sec
B takes time to complete one round = 400/16 = 25 sec
Both will meet at the starting point = LCM of 40, 25
Required time = LCM = 5 × 5 × 8 = 200 secs
∴ The answer is 200 seconds.
A thief is spotted by a constable from 200 m. When the constable starts the chase, the thief also starts running. If the speed of the constable is 8 km/h and thief runs at the speed of 6 km/h, then how far (in m) will the thief be able to run before he is overtaken?
Answer (Detailed Solution Below)
Relative Speed Question 10 Detailed Solution
Download Solution PDFGiven:
Distance between constable and thief = 200 m
Speed of constable = 8 km/h
Speed of thief = 6 km/h
Formula used:
Distance = relative speed × time
Calculation:
Distance = relative speed × time
⇒ 200 = (8 - 6) × (5/18) × time
⇒ 200 = 2 × (5/18) × time
⇒ Time = (200 × 18)/10
⇒ Time = 360 sec
Distance covered by thief = 6 × (5/18) × 360
⇒ 6 × 100 = 600 m
∴ The correct answer is 600 m.
A thief was spotted by a policeman from a distance of 225 metres. When the policeman started the chase, the thief also started running. If the speed of the thief was 11 km/h and that of the policeman was 13 km/h, how far would the thief have run, before the policeman caught up with him ?
Answer (Detailed Solution Below)
Relative Speed Question 11 Detailed Solution
Download Solution PDFGIVEN:
At a distance of 225 m policeman spotted a thief
speed of the thief is 11km/h
speed of policeman is 13 km/h :
CONCEPT USED:
Relative speed when the thief and policeman are running in the same direction = ( speed of policeman - speed of the thief)
Distance = Speed × Time
CALCULATION :
Relative speed = ( 13 - 11 ) = 2 km/h
To convert km/h into m/s we have to multiply it by 5/18.
⇒ 2 × 5/18 = 5/9 m/s.
\(Time = \frac{Distance}{Speed}\)
⇒ Time = \(\frac{225}{(5/9)}\) = 225 × \(\frac{9}{5}\) = 405 seconds.
The distance thief had run before he was caught by the policeman
⇒ 11× \(\frac{5}{18}\)× 405 = 1237.5 m
∴ The distance thief had run before he was caught by the policeman is 1237.5 m
Two athletes A and B are running on a circular track of length 1800 m from the same starting point at the same starting time, at the speeds of 9 m/s and 6 m/s, respectively. At how many distinct points will they meet while running in opposite directions?
Answer (Detailed Solution Below)
Relative Speed Question 12 Detailed Solution
Download Solution PDFGiven :
Speed of 1st person = 9 m/s
Speed of the 2nd person = 6 m/s
Circumference of the Track = 1800 m
Concept used :
Speed = Distance covered / Time taken
Calculation :
The time taken by the first person to complete a full lap is 1800 m / 9 m/s = 200 seconds.
The time taken by the second person to complete a full lap is 1800 m / 6 m/s = 300 seconds.
The LCM of 200 seconds and 300 seconds is 600 seconds, which means they will end up in the same initial positions after 600 seconds.
Let the two persons cross each other for the first time after x seconds.
Then, total distance covered by 1st person = 9x and the 2nd person = 6x
Now, the total distance covered by both the person = Circumference of the track
⇒ 9x + 6x = 1800m ⇒ 15x = 1800m ⇒ x = 120 s
∴ The two persons will cross each other for the first time after 120 seconds.
The two persons will cross each other again after 120 seconds, and then again after 120 seconds, and so on.
So in 600 seconds, they will meet = 600/120 = 5 times
Therefore, the two persons will cross each other at 5 distinct points on the track.
Shortcut Trick
S1 = 9 m/s and S2 = 6 m/s
S1/S2 = 3/2
They are running in opposite directions so they will meet each other at distinct points = 2 + 3 = 5
A train leaves Kazipet at 5 a.m. and reaches Bangalore at 3 p.m. Another B train leaves Bangalore at 7 a.m. and reaches Kazipet at 5 p.m. When do the two trains meet? Assume that the trains travels at equal uniform speeds.
Answer (Detailed Solution Below)
Relative Speed Question 13 Detailed Solution
Download Solution PDFLet speed be x km/hr
So, distance between stations = 10x km
When trains are travelling in opposite direction, relative speed = 2x km/hr.
Train A leaving at 5 am and train B at 7 am,
⇒ Distance travelled by A in 2 hrs = 2x
⇒ Remaining distance = 10x - 2x = 8x
⇒ Meeting time = 8x/2x = 4 hrs
∴ After 4 hrs, at 11 am train B will meet train A.A policeman noticed a thief from 300 m. The thief started running and the policeman was chasing him. The thief and the policeman ran at the speeds of 8 km/h and 9 km/h, respectively. What was the distance between them after 3 minutes?
Answer (Detailed Solution Below)
Relative Speed Question 14 Detailed Solution
Download Solution PDFGiven:
Distance between policeman and thief in the starting = 300 m
Speed of policeman = 9 km/hr
Speed of thief = 8 km/hr
Concept: /Formula:
If the speed of a policeman and thief is x km/hr and y km/hr, then
Relative speed, if same directions = (x – y) km/hr
Distance between them after n hrs = (x – y) × n
1 km/hr = 5/18 m/sec
1 min = 60 sec
Calculation:
3 min = 3 × 60 = 180 seconds
Distance between policeman and thief in starting = 300 m
Relative speed of policeman and thief, if same directions = (9 – 8) = 1 × (5/18) = (5/18) m/sec
Distance covered in 180 seconds = (5/18) × 180 = 50 m
Distance between them after 180 seconds= 300 – 50 = 250 m
∴ Distance between them after 3 min is 250 m.
In a circular race of 5000 m, starting from the same point, the speeds of two contestants A and B are 36 km/h and 54 km/h, respectively. The difference between the time taken (in seconds) to meet for the first time when they are running in the opposite directions and when they are running in the same direction?
Answer (Detailed Solution Below)
Relative Speed Question 15 Detailed Solution
Download Solution PDFGiven
Circular race length: 5000 m
Speed of A: 36 km/h (or 10 m/s)
Speed of B: 54 km/h (or 15 m/s)
Concept:
Time = Distance/Speed. In opposite directions, the speeds add up; in the same direction, they subtract.
Solution:
Time taken when running in opposite directions = 5000/(10 + 15) ⇒ 200 seconds
Time taken when running in the same direction = 5000/(15 - 10) ⇒ 1000 seconds
The difference in times = 1000 - 200 ⇒ 800 seconds
Therefore, the difference between the times taken to meet for the first time in opposite and the same directions is 800 seconds.