Speed Time and Distance MCQ Quiz - Objective Question with Answer for Speed Time and Distance - Download Free PDF

Given:

Downstream distance = 64 km

Time taken for downstream = 4 hours

Upstream distance = 48 km

Time taken for upstream = 6 hours

Formula used:

Speed = Distance ÷ Time

Speed downstream = (Speed of boat + Speed of current)

Speed upstream = (Speed of boat - Speed of current)

Calculations:

Speed downstream = 64 ÷ 4 = 16 km/hr

Speed upstream = 48 ÷ 6 = 8 km/hr

Let the speed of the boat in still water be 'b' km/hr and the speed of the current be 'c' km/hr.

Speed downstream = b + c = 16

Speed upstream = b - c = 8

Now, solving the equations:

b + c = 16

b - c = 8

Add the two equations:

(b + c) + (b - c) = 16 + 8

2b = 24

b = 12 km/hr

The speed of the boat in still water is 12 km/hr.

Now, the distance covered by the boat in 5 hours in still water is:

Distance = Speed × Time

Distance = 12 × 5 = 60 km

∴ The distance covered by the boat in 5 hours in still water is 60 km.

Given:

Distance covered by first bus = 320 km

Time taken by first bus = 8 hours

Speed of second bus = 25% more than first bus

Distance to be covered by second bus = 200 km

Formula used:

Speed = Distance / Time

Calculations:

Speed of first bus = 320 km / 8 hours = 40 km/h

Speed of second bus = 40 km/h + 25% of 40 km/h = 40 km/h + 10 km/h = 50 km/h

Time taken by second bus to cover 200 km = Distance / Speed

Time = 200 km / 50 km/h = 4 hours

∴ The time taken by the second bus to cover 200 km is 4 hours.

Calculation

Let speed of train P and Q be 5x m/sec. & 9x m/sec. respectively

ATQ,

[ (d+300) / 5x] =  [(d+700) / 9x]

So, 9d + 2700 = 5d + 3500

So, 4d = 800

So, d = 200

Calculation

Distance travelled by boat in downstream = 3x/5 km

Distance travelled by boat in upstream = [2x / 5] km

ATQ, [2x / 5(12 - 8)] − [3𝑥 / 5(12 + 8)] = 14

Or, [10x−3x] / 100 = 14

So, x = 200

Distance covered in downstream = 200 × [3 / 5] = 120

Given:

Speed of the train = 90 km/hr = (90 × 1000) / 3600 = 25 m/s

Time taken to pass the man = 10 seconds

Time taken to pass the bridge = 18 seconds

Formula Used:

Total Length of Train + Length of Bridge = Speed × Time to pass the bridge

Length of Train = Speed × Time to pass the man

Calculation:

Length of Train = Speed × Time to pass the man

⇒ Length of Train = 25 × 10

⇒ Length of Train = 250 m

Total Length of Train + Length of Bridge = Speed × Time to pass the bridge

⇒ 250 + Length of Bridge = 25 × 18

⇒ 250 + Length of Bridge = 450

⇒ Length of Bridge = 450 - 250

⇒ Length of Bridge = 200 m

The length of the bridge is 200 m.

Given

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.

Given:

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.

Given:

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.

Given:

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 = 

Average Speed = 207/5

Average Speed = 41.4 km/hr

∴ The average speed of whole journey is 41.4 km/h

Concept used:

Speed × time = distance

Calculation:

In the 1^st 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

Given:

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.

Given:

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 

⇒  = 

⇒ 2y = 5y - 200 

⇒ y = 200/3 = 66.67m 

∴ The distance from the starting point where both of them will meet is 66.67 m

Concept 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

Given:

Speed of train 1 = 80 km/h

Speed of train 2 = 95 km/h

Difference in distance = 180 km

Concept:

Distance = Speed × Time 

Solution:

Let the time of travelling be 't' hours

Distance travelled by train with speed 80 km/h = 80 × t

Distance travelled by train with speed 95 km/h = 95 × t 

According to the question, 

Difference in distance travelled by two train  = 180 km 

⇒ 95 t - 80t = 180 

⇒ 15t =  180 

⇒ t = 12 hours 

Distance between stations = 80 × 12 + 95 × 12  = 960 + 1140 = 2100km

Hence, the distance between Bangalore and Chennai is 2100 km .

Given:-

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