CMAT Time Speed and Distance Questions [Download PDF]

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Question 1: A train 350 m long takes 36 seconds to cross a man running at a speed of 5 km/h in the direction opposite to that of train. What is the speed of the train?

a) 30 km/h

b) 40 km/h

c) 24 km/h

d) 34 km/h

e) Other than those given as options

1) Answer (A)

Solution:

Let the speed of the train be x m/s
Speed of the man = 5km/hr = 1.388m/s
Relative speed of man when he is running in opposite direction = (x+1.388)
However train crossess him in 36 seconds = 350/36 =  9.722 m/s
x+1.388 = 9.722
x = 8.334 m/s
x = 30 km/hr

Question 2: A boat running downstream covers a distance of 24 km in 4 hours, while for covering the same distance upstreams it takes 6 hours. What is the speed of the boat in still water?

a) 5.5 kmph

b) 6 kmph

c) 3.5 kmph

d) Data inadequate

e) None of these

2) Answer (E)

Solution:

Let the speed of the boat be S and the speed of the stream be R.

So, 24 / 4 = 6 = S + R

24 / 6 = 4 = S – R

So, 2S = 10 => S = 5 and R = 1

So, speed of the boat in still water = 1 kmph

Question 3: A motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 km?

a) $2\frac{1}{4}$hours

b) $4\frac{1}{2}$hours

c) $4$ hours $5$ minutes

d) Cannot be determined

e) None of these

3) Answer (B)

Solution:

Distance = Speed $\times$ Time

Initial speed = 70 kmph

In first 2 hours, motor covers a distance = $70 \times 2 = 140~km$

Speed after 2 hours = 70 + 10 = 80 kmph

In the next 2 hours, it covers a distance = $80 \times 2 = 160~km$

Distance covered = 300 km

Now, the speed is 90 kmph

Remaining 45 km is covered in $\frac{45}{90}$ = 0.5 hr

Total time taken to cover 345 km = 2 + 2 + 0.5 = 4.5 hr

Question 4: A truck covers a certain distance in 12 h at the speed of 70 km/h. What is the average speed of a car which travels a distance of 120 km more than the truck in the same time ?

a) 76 km/h

b) 85 km/h

c) 82 km/h

d) 78 km/h

e) None of these

4) Answer (E)

Solution:

The distance travelled by the truck in 12 hours equals 12*70 = 840 km
Hence, the car travels 840 + 120 = 960 kms in 12 hours.

So, the average speed of the car equals $\frac{960}{12} = 80$ kmph

Question 5: A 420 m long train crosses a pole in 70 seconds. What is the speed of the train ?

a) 5 m/s

b) 7 m/s

c) 4.5 m/s

d) Cannot be determined

e) None of these

5) Answer (E)

Solution:

Time taken by the train to cross the pole is 70 seconds.
The length of the train is 420 metres.

Hence, the speed of the train is $\frac{420}{70}=6$ seconds.

Question 6: A boat running downstreams covers a distance of 16 km in 2 hours while for covering the same distance upstream it takes 4 hours. What is the speed of the boat in still water?

a) 4 kmph

b) 6 kmph

c) 8 kmph

d) Data inadequate

e) None of these

6) Answer (B)

Solution:

Let the speed of the boat in still water be B and the speed of the water be W.
So, speed of the boat downstream is B+W and the speed of the boat upstream is B-W.

From the information given, the speed of the boat downstream is 16/2 = 8 kmph
Speed of the boat upstream is 16/4 = 4 kmph

Hence, B+W = 8 and B-W =4
So, B = 6 kmph and W = 2 kmph

Question 7: A train running at the speed of 66 kmph crosses a signal pole in 18 seconds. What is the length of the train?

a) 330 meters

b) 300 metres

c) 360 metres

d) 320 metres

e) None of these

7) Answer (A)

Solution:

66 kmph = 66 *5/18 m/s

It takes 18 secs to cross the post. So, length = 66 * 18* 5/18 = 330 metres.

Question 8: Two cars A and B are running in the same direction. Car ‘A’ had already covered a distance of 60 kms, when car ‘B’ started running. The cars meet each other in 3 hours after car ‘B’ started running. What was the speed of car ‘A’ ?

a) 40 kmph

b) 60 kmph

c) 45 kmph

d) Cannot be determined

e) None of these

8) Answer (D)

Solution:

Let the speed of car A be ‘x’ kmph and the speed of car B be ‘y’ kmph.
By the time car B started running, car A covered 60 Km.

Distance covered by B in three hours is 3y
Distance covered by A in three hours is 3x

So, 3y = 3x + 60 or y=x+20
Hence, the speed of B is 20 kmph more than the speed of A. As we don’t know the speed of car B, we can’t find the exact speed of car A. We can just infer that the speed of car A is 20 kmph less than the speed of car B.

Question 9: A train running at a speed of 60 kmph crosses a platform double its length in 32.4 seconds. What is the length of the platform?

a) 108 metres

b) 240 meters

c) 360 meters

d) 90 meters

e) Cannot be determined

9) Answer (C)

Solution:

Let the length of the train be ‘x’ metres
Length of the platform = 2x
Distance travelled by the train = x + 2x = 3x
Speed of the train = 60 kmph = $60 \times \frac{5}{18}$ m/sec
Distance = Speed $\times$ Time
$3x = 60 \times \frac{5}{18} \times 32.4$
$x = 180$
The length of the platform = 2x = 360 m

Question 10: A person has to travel from point B in certain time. Travelling at a speed of 5 kmph he reaches 48 minutes late and while travelling at a speed of 8 kmph he reaches 15 minutes early. What is the distance from point A to point B?

a) 15 kms

b) 91 kms

c) 12 kms

d) 18 kms

e) 14 kms

10) Answer (E)

Solution:

Let the distance between A and B be ‘d’ km and time taken be ‘t’ hrs.
In both the cases, distance travelled is the same.
Distance = Speed $\times$ Time
Case (i) Time taken = 48 min late = (t + 0.8) hrs
$d = 5 \times (t + 0.8)$
Case (ii) Time taken = 15 min early = (t – 0.25) hrs
$d = 8 \times (t – 0.25)$
On equating them, we get
5t + 4 = 8t – 2
t = 2
Distance, d = 5 (2 + 0.8) = 14 km

Question 11: Ram and Shyam are travelling from point A to B, which are 60km apart. Travelling at a certain speed Ram takes one hour more than Shyam to reach point B. If Ram doubles his speed he will take 30 minutes less than Shyam to reach point B. At what speed was Ram driving from point A to B?

a) 15 kmph

b) 35 kmph

c) 30 kmph

d) 25 kmph

e) 20 kmph

11) Answer (E)

Solution:

Let the speed of Ram be ‘v’ kmph
Time taken by Shyam be ‘t’ hrs
Distance = Speed $\times$ Time
60 = v (t + 1)
After doubling the speed,
60 = 2v(t – 0.5)
Simplifying them, we get
v (t + 1) = 2v (t – 0.5)
t = 2
v = 60/3 = 20 kmph

Question 12: The respective ratio between speed of the boat upstream and speed of the boat downstream is 3 : 4. What is the speed of the boat in still water if it covers 70 km downstream in 3 hours 30 minutes? (in km/h)

a) 18

b) 18.5

c) 17

d) 17.5

e) 16

12) Answer (D)

Solution:

Let the speed of boat in still water and speed of river be B km/hr and R km/hr respectively

Speed of boat in downstream = (B+R)km/hr

Speed of boat in upstream = (B-R) km/hr

It is given that $\frac{B-R}{B+R} = \frac{3}{4}$

we get , B = 7 R

Now it is given that boat covers 70 km in 3.5 hours downstream

so ,

70 = (B+R)3.5

B+R = 20

R = 2.5 km/hr

B = 17.5 km/hr

Question 13: The time taken by a boat to travel a distance downstream is half the time taken by it to travel the same distance upstream. What is the speed of the boat downstream if it travels 7.5 km upstream in 1 hour 30 minutes ? (in km/h)

a) 7.5

b) 5

c) 9

d) 10

e) None of these

13) Answer (D)

Solution:

Let the speed of boat in still water and speed of river be B km/hr and R km/hr respectively .

Speed of boat in downstream = B+ R km/hr

Speed of boat in upstream = B-R km/hr = $\frac{7.5}{1.5}$= 5km/hr

Let the same distance travelled in upstream and downstream be D km

So ,

$\frac{D}{B-R}$ =2× $\frac{D}{B+R}$

B+R = 10 km/hr

Question 14: A car starts at 11 am from point A towards point B at 36 kmph while another car starts at 1 pm from point B towards A at 44 kmph. They cover a distance of 592 km till meeting. At what time will they meet each other ?

a) 8 pm

b) 6 : 30 pm

c) 7 : 30 pm

d) 5 : 30 pm

e) None of these

14) Answer (C)

Solution:

distance travelled by car which started from point A from 11 am to 1 pm is = 36 ×2 = 72 km

Now it is given that total distance is 592 km

Distance left to be covered = 592 – 72 = 520 km

Speed of car started from B = 44 km/hr

Soeed of car started from A = 36km/hr

Relative speed = 80 km/hr

Time taken = 520/80 = 6.5 hours

So the two cars will meet at 7.30 pm

Question 15: Two trains crosses each other in 14 sec when they are moving in opposite direction, and when they are moving in same direction they crosses each other in 3 min 2 sec. Find the speed of the faster train by what percent more than the speed of the slower train ?

a) 16.67%

b) 17.33%

c) 16.33%

d) 17.67%

e) 18.33%

15) Answer (A)

Solution:

let the speed of faster train be F m/s

And slower train be S m/s

When they move in same direction relative speed = (F -S) m/s

Time taken = 14 sec

When they move in opposite direction = (F+S) m/s

Time taken in this case = 182 sec

In both cases they are covering same distance

So , (F+S )× 14 = (F-S ) × 182

12 F = 14 S

F = $\frac{7}{6}$ S

so faster train is 1/6 more than the slower one which means it is 16.67% faster than the slower train.

Question 16: The time taken by a boat to travel; `x’ km upstream is twice the time taken by the same boat to travel `x’ km downstream. If speed of the boat in still water is 12 km/h. what is the speed of current ? (in km/h)

a) 3

b) 4

c) 3.5

d) 4.5

e) None of these

16) Answer (B)

Solution:

Distance travelled by boat = $x$ km

Let speed of current = $y$ km/h

Speed of boat = 12 km/h

=> Downstream speed = $(12 + y)$ km/h and upstream speed = $(12 – y)$ km/h

Acc. to ques, time taken by a boat to travel; `x’ km upstream is twice the time taken by the same boat to travel `x’ km downstream

=> $\frac{x}{12 – y} = 2 \times \frac{x}{12 + y}$

=> $\frac{1}{12 – y} = \frac{2}{12 + y}$

=> $12 + y = 24 – 2y$

=> $y + 2y = 3y = 24 – 12$

=> $y = \frac{12}{3} = 4$ km/h

Question 17: The ratio between speed of a boat downstream and speed of the boat upstream is 7 : 5 respectively. If the boat travels a distance of 63 km downstream in 3 hours, what is the speed of the boat in still water ? (in km/h)

a) 20 km/h

b) 16 km/h

c) 14 km/h

d) 12 km/h

e) 18 km/h

17) Answer (E)

Solution:

Le the speed of boat be B km/hr and speed of river be R km/hr

Speed of boat in downstream = (B + R) km/hr

Speed of boat in upstream = (B- R)km/hr

It is given that $\frac{B+R}{B-R}$ = $\frac{7}{5}$

B = 6R………..(1)

Distance travelled downstream = 63 km

Time taken = 3 hr

63 = (B+R)3

B+R = 21 ……….(2)

From equation 1 and 2

R = 18 km/hr

Question 18: The speed of a man is 3/4 th the speed of a bicycle. The bicycle covers 192 m. in 8 seconds. How much time will the man take to cover 54 m. ?

a) 3 seconds

b) 4 seconds

c) 7 seconds

d) 5 seconds

e) None of these

18) Answer (A)

Solution:

Speed of Bicycle = $\frac{192}{8}$ = 24 m/s

Speed of Man = $\frac{3}{4}\times24$

Speed of Man = 18 m/s

Distance to be covered by Man = 54 m

Time taken by Man = $\frac{54}{18}$ = 3 sec

Question 19: A bus covers 572 kms in .13 hours. What is the speed of the bus ?

a) 40 km/hr

b) 44 km/hr

c) 43 km/hr

d) 47 km/hr

e) None of these

19) Answer (B)

Solution:

Using,

Distance = Speed x Time

572 = Speed x 13

Speed = 44 km/hr

Question 20: Two pipes can fill a tank in 10 hours and 16 hours respectively. A third pipe can empty the tank in 32 hours. If all the three pipes are opened simultaneously then in how much time the tank will be full ? (in hours)

a) $7\frac{11}{21}$

b) $7\frac{13}{21}$

c) $8\frac{4}{21}$

d) $6\frac{5}{14}$

e) $8\frac{9}{14}$

20) Answer (B)

Solution:

Total quantity = 160 units
Speed pipe 1 = 16 $\frac{units}{hours}$

Speed pipe 2 = 10 $\frac{units}{hours}$

Speed pipe 3 = 5 $\frac{units}{hours}$

Time reqd = Total Units / [Speed (pipe 1 + pipe 2) – Speed Pipe 3]

Time = 160/21 = 7 $\frac{13}{21}$ hours

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