Speed Time and Distance MCQ Quiz - Objective Question with Answer for Speed Time and Distance - Download Free PDF
Last updated on Mar 19, 2025
Latest Speed Time and Distance MCQ Objective Questions
Speed Time and Distance Question 1:
Nikita travels by a motorboat down the river to her school and back. With the speed of the river remaining unchanged, if she doubles the speed of her motorboat, her total travel time decreases by 75%. What is the ratio of the original speed of the motorboat to the speed of the river?
Answer (Detailed Solution Below)
Speed Time and Distance Question 1 Detailed Solution
Let us take the speed of the boat and river to be \( b \) and \( x \) respectively and let the distance be \( d \).
As per the condition in the question, \( \frac{d}{x + b} \) is the normal time taken. \( \frac{d}{2x + b} \) is the special time taken i.e. if the speed gets doubled.
Since the time gets reduced by 75%, \( \frac{1}{4} \left[ \frac{d}{x + b} + \frac{d}{x - b} \right] = \left[ \frac{d}{2x + b} + \frac{d}{2x - b} \right] \)
We have to find the ratio of the speed of the motor boat to the speed of the river = \( \frac{x}{b} \)
Let us divide throughout by \( b \) and assume \( \frac{x}{b} = k \)
\( \frac{1}{k + 1} + \frac{1}{k - 1} = 4\left[\frac{1}{2k + 1} + \frac{1}{2k - 1}\right] \)
Solving for \( k \), we get: \( 2k \times (k^2 - 1) = 16k \times \left(k^2 - 1\right) \)
Hence, the ratio of the original speed of the motor boat to the speed of the river is equal to: \( \frac{\sqrt{7}}{2} \)
Speed Time and Distance Question 2:
Train ‘P’, running with a speed of 144 km/h, crosses a pole in 17 seconds. If the time taken by train ‘P’ to cross train ‘Q’ running with a speed of 72 km/h and coming from the opposite direction is 22.8 seconds, then find the length of train 'Q'.
Answer (Detailed Solution Below)
Speed Time and Distance Question 2 Detailed Solution
Train P crosses a pole in 17 seconds. The length of Train P is equal to the distance it covers in 17 seconds.
Speed of Train P = 144 km/h
Convert speed to m/s:
144 × 5/18 = 40 m/s
Length of Train P = Speed × Time
Length of Train P = 40 × 17 = 680 m
Train P and Train Q are moving in opposite directions. Their relative speed is the sum of their individual speeds.
Speed of Train P = 144 km/h = 40 m/s
Speed of Train Q = 72 km/h
Convert speed to m/s:
72 × 5/18 = 20 m/s
Relative speed = 40 + 20 = 60 m/s
Train P takes 22.8 seconds to cross Train Q. The combined length of the two trains is equal to the distance covered at the relative speed in 22.8 seconds.
Combined Length = Relative Speed × Time = 60 × 22.8 = 1368 m
The combined length of Trains P and Q is 1368 m, and the length of Train P is 680 m. Therefore, the length of Train Q is:
Length of Train Q = Combined Length Length of Train P = 1368 - 680 = 688 m
Thus, the length of Train Q is 688 meters.
Speed Time and Distance Question 3:
Time taken by a boat is two hour less than when the boat cover 72 km downstream than time taken by the boat to cover 72 km upstream. If speed of stream is 3 km/hr. Find the upstream speed?
Answer (Detailed Solution Below)
Speed Time and Distance Question 3 Detailed Solution
Let speed of boat is x km /hr.
so, ATQ, [72 / (x - 3) ] - [ 72 / (x + 3)] 2
or, x2 - 9 = 36 × 6 = 216
or, x2 = 225
or, x = 15
so, speed of boat is 15 km /hr.
upstream speed is 15 - 3 = 12 km /hr
Speed Time and Distance Question 4:
A Train travel 420 km at p km/hr and remaining 420 km at 140 km/hr. Total time taken by train to cover the whole distance is 6 hour 30 minutes. Find the time taken by train to cover 600 km at p km/hr?
Answer (Detailed Solution Below)
Speed Time and Distance Question 4 Detailed Solution
Train cover 420 km distance at 140 km /hr.
so, Time taken = 420 /140 = 3 hour.
Time travel by train at p km/hr speed is 6.5 - 3 = 3.5
Distance travel at p km/hr is 420 km.
so, p = 420 / 3.5 = 120 km /hr
so, time taken to cover 600 km distance at p km /hr is = 600 / 120 = 5 hour.
Speed Time and Distance Question 5:
When Shreya increases her speed from 20 km/h to 25 km/h, she takes one hour less than the usual time to cover a certain distance. What is the usual distance covered by her?
Answer (Detailed Solution Below)
Speed Time and Distance Question 5 Detailed Solution
Here, the distance traveled by Shreya is constant in both the cases.
So, \(20 \times t = 25 \times (t - 1) = D\)
\( \Rightarrow 20t = 25t - 25\)
\( \Rightarrow 5t = 25\)
\( \Rightarrow t = 5 \text{ hrs. So, Distance travelled} = 20 \times 5 = 100 \text{ Km.}\)
Top Speed Time and Distance MCQ Objective Questions
A train of length 400 m takes 15 seconds to cross a train of length 300 m traveling at 60 km per hour from the opposite direction along a parallel track. What is the speed of the longer train, in km per hour?
Answer (Detailed Solution Below)
Speed Time and Distance Question 6 Detailed Solution
Download Solution PDFGiven
Length of first train (L1) = 400 m
Length of second train (L2) = 300 m
Speed of second train (S2) = 60 km/hr
Time taken to cross each other (T) = 15 s
Concept:
Relative speed when two objects move in opposite directions is the sum of their speeds.
Calculations:
Let the speed of the first train = x km/hr
Total length = 300 + 400
Time = 15 sec
According to the question:
700/15 = (60 + x) × 5/18
28 × 6 = 60 + x
x = 108 km/hr.
Therefore, the speed of the longer train is 108 km per hour.
Running at a speed of 60 km per hour, a train passed through a 1.5 km long tunnel in two minutes, What is the length of the train ?
Answer (Detailed Solution Below)
Speed Time and Distance Question 7 Detailed Solution
Download Solution PDFGiven:
Speed is 60 km per hour,
Train passed through a 1.5 km long tunnel in two minutes
Formula used:
Distance = Speed × Time
Calculation:
Let the length of the train be L
According to the question,
Total distance = 1500 m + L
Speed = 60(5/18)
⇒ 50/3 m/sec
Time = 2 × 60 = 120 sec
⇒ 1500 + L = (50/3)× 120
⇒ L = 2000 - 1500
⇒ L = 500 m
∴ The length of the train is 500 m.
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)
Speed Time and Distance Question 8 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.
In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m. By what distance does Anil beat Charles?
Answer (Detailed Solution Below)
Speed Time and Distance Question 9 Detailed Solution
Download Solution PDFGiven:
In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m.
Concept used:
Time × Speed = Distance
Calculation:
According to the question,
Anil goes 1500m while Bakul goes (1500 - 150) i.e. 1350m.
Ratio of speed of Anil and Bakul = 1500 : 1350 = 10 : 9 = 200 : 180
According to the question,
Bakul goes 1500m while Charlie goes (1500 - 75) i.e. 1425m.
Ratio of speed of Bakul and Charlie = 1500 : 1425 = 20 : 19 = 180 : 171
So, the ratio of the speeds of Anil, Bakul and Charlie = 200 : 180 : 171
Let the speeds of Anil, Bakul and Charlie be 200k, 180k and 171k m/s respectively.
Time taken by Anil to finish the race = 1500/200k = 7.5/k seconds
Now, Anil beats Charlie by = (200 - 171)k ×7.5/k = 217.5m
∴ Anil beat Charlie by 217.5m.
Shortcut Trick
In a 1500 m race, Anil beats Bakul by 150 m
When Anil completes the race, Bakul covered (1500 - 150) = 1350 m
In a 1500 m race Charles is 75 m behind Bakul
So, in 1350 m race Charles is 75/1500 × 1350 = 67.5 m behind Bakul
So, Charles is (67.5 + 150) = 217.5 m behind from Anil in 1500 m race
∴ Anil beat Charlie by 217.5m.
A man travels from A to B at a speed of 36 km/hr in 74 minutes and he travels a distance from B to C with a speed of 45 km/hr in 111 minutes. Find the average speed of whole journey.
Answer (Detailed Solution Below)
Speed Time and Distance Question 10 Detailed Solution
Download Solution PDFGiven:
A man travels from A to B at a speed of 36 km/hr in 74 minutes and he travels a distance from B to C with a speed of 45 km/hr in 111 minutes.
Formula used:
Average speed = Total distance/Total time taken
Calculation:
Time taken = 74 min : 111 min [given]
Ratio of Time taken = 2 : 3
Average Speed = \(\frac{{36\ \times\ 2\ +\ 45\ \times\ 3}}{{2\ +\ 3}}\)
Average Speed = 207/5
Average Speed = 41.4 km/hr
∴ The average speed of whole journey is 41.4 km/h
Geeta runs 5/2 times as fast as Babita. In a race, if Geeta gives a lead of 40 m to Babita, find the distance from the starting point where both of them will meet (correct up to two decimal places).
Answer (Detailed Solution Below)
Speed Time and Distance Question 11 Detailed Solution
Download Solution PDFGiven:
Geeta runs 5/2 times as fast as Babita
Geeta gives a lead of 40 m to Babita
Formula Used:
Distance = Speed × Time
Calculation:
Let the speed of Babita be 2x
⇒ Speed of Geeta = (5/2) × 2x = 5x
Let the distance covered by Geeta be y meters
⇒ Distance covered by Babita = (y - 40) meters
As time is constant, distance is directly proportional to speed
⇒ \(\frac{2x}{5x}\) = \(\frac{y-40}{y}\)
⇒ 2y = 5y - 200
⇒ y = 200/3 = 66.67m
∴ The distance from the starting point where both of them will meet is 66.67 m
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)
Speed Time and Distance Question 12 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
A boat goes 20 km upstream and 44 km downstream in 8 hours. In 5 hours, it goes 15 km upstream and 22 km downstream. Determine the speed of the boat in still water.
Answer (Detailed Solution Below)
Speed Time and Distance Question 13 Detailed Solution
Download Solution PDFConcept used:
If upstream speed = U and downstream speed = D, then speed of boat = (U + D)/2
Calculation:
According to the question,
20/U + 44/D = 8 … (i)
15/U + 22/D = 5 … (ii)
Multiply by 2 the equation (ii) then subtract from 1 we get
20/U + 44/D = 8
30/U + 44/D = 10
- 10/U = - 2
⇒ U = 5 km/hr
Putting the value in equation (i), we get D = 11
So, the speed of boat = (U + D)/2 = (5 + 11)/2 = 8 km/hr
∴ The correct answer is 8 km/hr
Two trains, one 152.5 m long and the other 157.5 m long, coming from opposite directions crossed each other in 9.3 seconds. The combined speed of the two trains every hour would then be:
Answer (Detailed Solution Below)
Speed Time and Distance Question 14 Detailed Solution
Download Solution PDFGiven:-
Train1= 152.5m
Train2= 157.5m
Time = 9.3 sec
Calculation:-
⇒ Total distance to be covered = total length of both the trains
= 152. 5 + 157.5
= 310 m
Total time taken = 9.3 sec
Speed = distance/time
= (310/9.3) m/sec
= (310/9.3) × (18/5)
= 120 km/hr
∴ The combined speed of the two trains every hour would then be 120 km/hr.
Alternate Method When two trains are moving in opposite direction-
Let the speed of ine is 'v' and the second is 'u'
∴ Combined speed = v + u
Total distance = 152.5 + 157.5
= 310 m
∴ Combined speed = Total distance/total time
⇒ (v + u) = 310/9.3
⇒ (v + u) = 33.33 m/s
⇒ (v + u) = 33.33 × (18/5)
⇒ (v + u) = 120 km/hr
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)
Speed Time and Distance Question 15 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 m