time speed and idistance

SOURAV SIR’S CLASSES 98367 93076

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TIME, SPEED & DISTANCE

Important Formulae:

i) Speed=Distance/Time

ii) Time=Distance/speed

iii) Distance = speed*time

iv) 1kmhr=5/18ms

v) 1ms=18/5Kmhr

vi) If the ratio of the speed of A and B is a:b,then the ratio of the time taken by them to cover

the same distance is 1/a:1/b or b:a

vii) Suppose a man covers a distance at x kmph and an equal distance at y kmph,

then the AVERAGE SPEED during the whole journey is (2xy/x+y) kmph

Out of time, speed and distance we can compute any one of the quantities when we happen to

know the other two. For example, suppose we drive for 2 hours at 30 miles per hour, for a

total of 60 miles.

If we know the time and the speed, we can find the distance:

2 hour * 30 miles/hour=60 miles

If we know the time and the distance, we can find the speed:

60 miles2 hours=30miles/hour

Distance is directly proportional to Velocity when time is constant:

Example: A car travels at 30km/hr for the first 2 hrs& then 40km/hr for the next 2hrs. Find

the ratio of distance travelled

S1S2=V1V2=34

Example: Two cars leave simultaneously from points A & B (1.km apart) & they meet at a

point 40 km from A. What is VaVb?

Time is constant so V1V2=S1S2=4060=46

Example: A train meets with an accident and moves at (34)th its original speed. Due to this,

it is 20 min late. Find the original time for the journey beyond the point of accident?

BYSOURAV DAS


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Method1: Think about 2 diff. situations, 1st with accident and another w/o accident. As

distance in both the cases is constant

So V1V2=T2T1

=>V1[34*V1]=T1+20T1

=> 43=T1+20T1 =>T1=60

Method 2: Velocity decreases by 25% (34 of original speed => decrement by 14) so time

will increase by 33.3% (43 of original time => increment by 13)

now, 33.3%=20 min =>1.%=60 min

Relative Speed:

Case1: Two bodies are moving in opposite directions at speed V1 & V2 respectively. The

relative speed is defined as Vr=V1+V2

Case2: Two bodies are moving in same directions at speed V1 & V2 respectively. The

relative speed is defined as Vr=|V1–V2|

Train Problems:

The basic equation in train problem is the same Speed=DistanceTime

The following things need to be kept in mind while solving the train related problems.

When the train is crossing a moving object, the speed has to be taken as the relative

speed of the train with respect to the object.

The distance to be covered when crossing an object, whenever trains crosses an object

will be equal to: Length of the train + Length of the object

Boats & Streams:

Let U= Velocity of the boat in still water

V=Velocity of the stream.

While moving in upstream, distance covered, S=(U−V)T

In case of downstream, distance covered ,S=(U+V)T

Clock:

For clock problems consider the clock as a circular track of 60km.

Min. hand moves at the speed of 60km/hr (think min. hand as a point on the track) and hour

hand moves at 5km/hr and second hand at the speed of 36. km/hr.

Relative speed between HOUR hand and MINUTE hand = 55


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1. A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?

A. 3.6 B. 7.2

C. 8.4 D. 10

Answer & Explanation

Answer: Option B

Explanation:

Speed =

600

m/sec. 5 x 60

= 2 m/sec.

Converting m/sec to km/hr

=

2 x 18

km/hr 5

= 7.2 km/hr.

2. An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the

same distance in 1 hours, it must travel at a speed of:

A. 300 kmph B. 360 kmph

C. 600 kmph D. 720 kmph


Answer: Option D

Explanation:

Distance = (240 x 5) = 1200 km.

Speed = Distance/Time

Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]

Required speed =

1200 x 3

km/hr = 720 km/hr.

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3. If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more.

The actual distance travelled by him is:

A. 50 km B. 56 km

C. 70 km D. 80 km

Answer: Option A

Explanation:

Let the actual distance travelled be x km.

Then, x

= x + 20

10 14

14x = 10x + 200

4x = 200

x = 50 km.

4. A train can travel 50% faster than a car. Both start from point A at the same time and

reach point B 75 kms away from A at the same time. On the way, however, the train lost

about 12.5 minutes while stopping at the stations. The speed of the car is:




Answer: Option C

Explanation:

Let speed of the car be x kmph.

Then, speed of the train = 150

x =

3 x

kmph. 100 2

75 -

75 =

125

x (3/2)x 10 x 60

75 -

50 =

5

x x 24

x =

25 x24

= 120 kmph.


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5. Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45

kmph. For how many minutes does the bus stop per hour?

A. 9 B. 10

C. 12 D. 20


Answer: Option B

Explanation:

Due to stoppages, it covers 9 km less.

Time taken to cover 9 km =

9 x 60

min = 10 min.

6. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed

for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The

duration of the flight is:

A. 1 hour B. 2 hours

C. 3 hours D. 4 hours


Answer: Option A

Explanation:

Let the duration of the flight be x hours.

Then, 600

- 600

= 200 x x + (1/2)

600 -

1200 = 200

x 2x + 1

x(2x + 1) = 3

2x2 + x - 3 = 0

(2x + 3)(x - 1) = 0

x = 1 hr. [neglecting the -ve value of x]


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7. A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21

km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

A. 220 km B. 224 km

C. 230 km D. 234 km


Answer: Option B

Explanation:

(1/2)x +

(1/2)x = 10

21 24

x +

x = 20

21 24

15x = 168 x 20

x =

168 x 20

= 224 km. 15

8. The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4

hours, then the speed of the first train is:

A. 70 km/hr B. 75 km/hr

C. 84 km/hr D. 87.5 km/hr


Answer: Option D

Explanation:

Let the speed of two trains be 7x and 8x km/hr.

Then, 8x =

400

= 100 4

x =

100

= 12.5 8

Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.


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9. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The

average speed for the first 320 km of the tour is:

A. 35.55 km/hr B. 36 km/hr

C. 71.11 km/hr D. 71 km/hr


Answer: Option C

Explanation:

Total time taken =

160 +

160

hrs. =

9 hrs.

64 80 2

Average speed =

320 x 2

km/hr = 71.11 km/hr.

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10.

A car travelling with of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the

actual speed of the car.

A. 17 6

km/hr 7

B. 25 km/hr

C. 30 km/hr D. 35 km/hr


Answer: Option D

Explanation:

Time taken = 1 hr 40 min 48 sec = 1 hr 40 4

min = 1 51

hrs = 126

hrs. 5 75 75

Let the actual speed be x km/hr.

Then, 5 x x

126 = 42

7 75

x =

42 x 7 x 75

= 35 km/hr. 5 x 126

11. In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay

doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:


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A. 5 kmph B. 6 kmph

C. 6.25 kmph D. 7.5 kmph


Answer: Option A

Explanation:

Let Abhay's speed be x km/hr.

Then, 30

- 30

= 3 x 2x

6x = 30

x = 5 km/hr.

12. Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. if he travels

at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must

he travel to reach A at 1 P.M.?




Answer: Option C

Explanation:

Let the distance travelled by x km.

Then, x

- x

= 2 10 15

3x - 2x = 60

x = 60 km.

Time taken to travel 60 km at 10 km/hr =

60

hrs = 6 hrs.

10


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So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.

Required speed =

60

kmph. = 12 kmph.

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13. It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It

takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the

speed of the train to that of the cars is:

A. 2 : 3 B. 3 : 2

C. 3 : 4 D. 4 : 3


Answer: Option C

Explanation:

Let the speed of the train be x km/hr and that of the car be y km/hr.

Then, 120

+ 480

= 8 1

+ 4

= 1

....(i) x y x y 15

And, 200

+ 400

= 25

1

+ 2

= 1

....(ii) x y 3 x y 24

Solving (i) and (ii), we get: x = 60 and y = 80.

Ratio of speeds = 60 : 80 = 3 : 4.

14. A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr

and partly on bicycle @ 9 km/hr. The distance travelled on foot is:

A. 14 km B. 15 km

C. 16 km D. 17 km


Answer: Option C

Explanation:

Let the distance travelled on foot be x km.


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Then, distance travelled on bicycle = (61 -x) km.

So, x

+ (61 -x)

= 9 4 9

9x + 4(61 -x) = 9 x 36

5x = 80

x = 16 km.

15. A man covered a certain distance at some speed. Had he moved 3 kmph faster, he would

have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40

minutes more. The distance (in km) is:

A. 35 B. 36 2

3

C. 37 1

2

D. 40


Answer: Option D

Explanation:

Let distance = x km and usual rate = y kmph.

Then, x

- x

= 40

2y(y + 3) = 9x ....(i) y y + 3 60

And, x

- x

= 40

y(y - 2) = 3x ....(ii) y -2 y 60

On dividing (i) by (ii), we get: x = 40.

16. A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6

Kmph, he reaches there 8 minutes earlier. How far is the office from his house?

A.) 3 1/5 Km B.) 2 1/5 Km

C.) 4 1/5 Km D.) 5 1/5 Km


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Show Answer

Answer: Option 'A'

Formula = S1*S2/S2-S1 * T1+T2/60

= 4*6/2 * 16/6

= 24/2 * 16/60

= 8 * 2/5

= 16/5 = 3 1/5 Km

17. A car takes 6 hours to cover a distance of 540 Km. how much should the speed in

Kmph be maintained to cover the same direction in 3/2th of the previous time?

A.) 6o Kmph B.) 62 Kmph

C.) 75 Kmph D.) 77 Kmph

Show Answer

Answer: Option 'A'

Time = 6

Distence = 540

3/2 of 6 hours = 6 * 3/2 = 9 Hours

Required speed = 540/9 = 60 Kmph

18. Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th

of time then, What speed should he maintain to cover the remaining distance in the

remaining time?

A.) 13 Kmph B.) 14 Kmph


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Show Answer

Answer: Option 'C'

Total distance = 8 Km

Total time = 50 Km

Time taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours

Remaining distance = 8 - 3 = 5 Km

Required speed = 5/1/3 = 15 Kmph

19. A man covers a distance of 180 Km at 72 Kmph and next 190km at 88 Kmph. what

is his average speed For his whole journey of 370 Km?

A.) 79.2 Kmph B.) 79.3 Kmph

C.) 77.25 Kmph D.) 78.5 Kmph

Show Answer

Answer: Option 'A'

Formula = 2*F.S*S.P/F.S+S.P

= 2*72*88/88+72

=79.2 Kmph

20. An aeroplane covers a certain distance of 420 Kmph in 6 hours. to cover the same

distance in 4 2/3 hours, it Must travel at a speed of

A.) 580 Kmph B.) 550 Kmph


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Show Answer

Answer: Option 'C'

Speed of aeroplane = 420 Kmph

Distance travelled in 6 hours

= 420 * 6 = 2520 Km

Speed of aeroplane to acver 2520 Km in 14/3

= 2520*3/14 = 540 Km

21. If a man walks 24 Km at 8 Kmph, he will be late by 25min. if he walks 12 Kmph,

how early the fixed time Will he reach?

A.) 30 minutes B.) 25 minutes

C.) 40 minutes D.) 35 minutes

Show Answer

Answer: Option 'D'

Time taken to cover 24 Km at the speed of 8 Kmph = 24/8 = 3 hours

Thus, right time was 2 hours 35 mintes

Now, time taken to cover 20 Km at the speed as 12 Kmph = 2 hours

Required time = 2 hours 35 minutes - 2 hours

= 35 minutes


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Aptitude Questions for Time & Distance Problems

Aptitude Questions With .wers for Time & Distance Problems

22) A train covers a distance in 50 min ,if it runs at a speed

of 48kmph on an average.The speed at which the train must run

to reduce the time of journey to 40min will be.

Solution::

Time=50/60 hr=5/6hr

Speed=48mph

distance=S*T=48*5/6=40km

time=40/60hr=2/3hr

New speed = 40* 3/2 kmph= 60kmph

23) Vikas can cover a distance in 1hr 24min by covering 2/3 of

the distance at 4 kmph and the rest at 5kmph.the total

distance is?

Solution::

Let total distance be S

total time=1hr24min

A to T :: speed=4kmph

diistance=2/3S

T to S :: speed=5km

distance=1-2/3S=1/3S

21/15 hr=2/3 S/4 + 1/3s /5

84=14/3S*3

S=84*3/14*3

= 6km

24) walking at ¾ of his usual speed ,a man is late by 2 ½ hr.

the usual time is.

Solution::

Usual speed = S

Usual time = T

Distance = D


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New Speed is ¾ S

New time is 4/3 T

4/3 T – T = 5/2

T=15/2 = 7 ½

25) A man covers a distance on scooter .had he moved 3kmph

faster he would have taken 40 min less. If he had moved

2kmph slower he would have taken 40min more.the distance is.

Solution::

Let distance = x m

Usual rate = y kmph

x/y – x/y+3 = 40/60 hr

2y(y+3) = 9x ————–1

x/y-2 – x/y = 40/60 hr y(y-2) = 3x —————–2

divide 1 & 2 equations

by solving we get x = 40

26) Excludingstoppages,the speed of the bus is 54kmph and

including stoppages,it is 45kmph.for how many min does the bus

stop per hr.

Solution::

Due to stoppages,it covers 9km less.

time taken to cover 9 km is [9/54 *60] min = 10min

27) Two boys starting from the same place walk at a rate of

5kmph and 5.5kmph respectively.wht time will they take to be

8.5km apart, if they walk in the same direction

Solution::


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The relative speed of the boys = 5.5kmph – 5kmph = 0.5 kmph

Distance between them is 8.5 km

Time= 8.5km / 0.5 kmph = 17 hrs

28) 2 trains starting at the same time from 2 stations 2.km

apart and going in opposite direction cross each other ata

distance of 110km from one of the stations.what is the ratio of

their speeds.

Solution::

In same time ,they cover 110km & 90 km respectively

so ratio of their speed =110:90 = 11:9

29) Two trains start from A & B and travel towards each other at

speed of 50kmph and 60kmph resp. At the time of the meeting the

second train has traveled 120km more than the first.the distance

between them.

Solution::

Let the distance traveled by the first train be x km

then distance covered by the second train is x + 120km

x/50 = x+120 / 60

x= 6.

so the distance between A & B is x + x + 120 = 1320 km

30) A thief steals a ca r at 2.30pm and drives it at 60kmph.the

theft is discovered at 3pm and the owner sets off in another car

at 75kmph when will he overtake the thief

Solution::

Let the thief is overtaken x hrs after 2.30pm

distance covered by the thief in x hrs = distance covered by

the owner in x-1/2 hr

60x = 75 ( x- ½)

x= 5/2 hr

thief is overtaken at 2.30 pm + 2 ½ hr = 5 pm


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31) In covering distance,the speed of A & B are in the ratio

of 3:4.A takes 30min more than B to reach the destion.The time

taken by A to reach the destinstion is.

Solution::

Ratio of speed = 3:4

Ratio of time = 4:3

let A takes 4x hrs,B takes 3x hrs

then 4x-3x = 30/60 hr

x = ½ hr

Time taken by A to reach the destination is 4x = 4 * ½ = 2 hr

32) In a one km race A gives B a start of 100m and in a one km race B gives a start of 80 m

to C. In a 1 km race who will win and by how much distance from the worst performer

between two losers?

Solution::

Ratio of speeds of A:B = 1000:900 = 100:90

Ratio of speeds of B:C = 1000:920 = 100:92

Therefore, when A moves 1000m , B moves 900 m and when B moves 900m, C moves

828m

Thus,

Since , C moves 8 % less than B in the same time . Thus, C is the worst performer and A will

win by him by 172 m


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PART 2

33. The speed of a car increases by 2 kms after every one hour. If the distance travelling in

the first one hour was 35 kms. what was the total distance travelled in 12 hours?

A) 456 kms B) 482 kms

C) 552 kms D) 556 kms

Explanation:

Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms)

This is an A.P with first term, a=35, number of terms,

n= 12,d=2.

Required distance = 12/2[2 x 35+{12-1) x 2]

=6(70+23)

= 552 kms.

34. A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the

bridge (in metres) is

A) 600 B) 750

C) 1000 D) 1250

Answer &ExplanationAnswer: D) 1250

Explanation:

speed = (5x5/18)m/sec

= 25/18 m/sec.

Distance covered in 15 minutes = (25/18 x 15 x 60)m

= 1250 m.

35. A thief is noticed by a policeman from a distance of 200 m. The thief starts running and

the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km

per hour respectively. What is the distance between them after 6 minutes?


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A) 100 m B) 150 m

C) 190 m D) 200 m

Answer &ExplanationAnswer: A) 100 m

Explanation:

Relative speed of the thief and policeman = (11 – 10) km/hr = 1 km/hr

Distance covered in 6 minutes = km = km = 100 m

Distance between the thief and policeman = (200 – 100) m = 100 m.

36. Two horses start trotting towards each other, one from A to B and another from B to A.

They cross each other after one hour and the first horse reaches B, 5/6 hour before the

second horse reaches A. If the distance between A and B is 50 km. what is the speed of the

slower horse?

A) 30 km/h B) 15 km/h

C) 25 km/h D) 20 km/h

Answer &ExplanationAnswer: D) 20 km/h

Explanation:

If the speed of the faster horse be and that of slower horse be then

and

Now, you can go through options.

The speed of slower horse is 20km/h

Since, 20+30=50

and

37. The distance between two cities A and B is 330 Km. A train starts from A at 8 a.m. and

travel towards B at 60 km/hr. Another train starts from B at 9 a.m and travels towards A at

75 Km/hr. At what time do they meet?

A) 10 a.m B) 10.30 a.m

C) 11 a.m D) 11.30 a.m

Answer &ExplanationAnswer: C) 11 a.m


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Explanation:

Suppose they meet x hrs after 8 a.m

then,

[Distance moved by first in x hrs] + [Distance moved by second in (x-1) hrs] = 330.

Therefore, 60x + 75(x-1) = 330.

=> x=3.

So,they meet at (8+3) i.e, 11a.m.

38. A man takes 6 hours 15 minutes in walking a distance and riding back to the starting

place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both

ways, is

A) 4 hours B) 4 hours 30 minutes

C) 4 hours 45 minutes D) 5 hours

Answer &ExplanationAnswer: C) 4 hours 45 minutes

Explanation:

Time taken in walking both ways = 7 hours 45 minutes --------(i)

Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)

By equation (ii)*2 -(i), we have

Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes

39. A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The

average speed for the first 320 km of the tour is

A) 35.55 km/hr B) 36 km/hr

C) 71.11 km/hr D) 71 km/hr

Answer &ExplanationAnswer: C) 71.11 km/hr

Explanation:

Total time taken = (160/64 + 160/8)hrs

= 9/2 hrs.

Average speed = (320 x 2/9) km.hr

= 71.11 km/hr.


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40. A machine puts c caps on bottles in m minutes. How many hours will it take to put caps

on b bottles

A) 60bm/c B) bm/60c

C) bc/60m D) 60b/cm

Answer &ExplanationAnswer: B) bm/60c

Explanation:

Substitute sensible numbers and work out the problem. Then change the numbers back to

letters. For example if the machine puts 6 caps on bottles in 2 minutes, it will put 6 /2 caps on

per minute, or (6 /2) x 60 caps per hour. Putting letters back this is 60c/m.If you divide the

required number of caps (b) by the caps per hour you will get time taken in hours. This gives

bm/60c

41. The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4

hours, then the speed of the first train is ?

A) 83.5 km/hr B) 84.5 km/hr

C) 86.5 km/hr D) 87.5 km/hr

Answer &ExplanationAnswer: D) 87.5 km/hr

Explanation:

Let the speeds of two trains be 7X and 8X km/hr.

8x =

=> x= 12.5 km/hrX=4004=>X=12.5Km/hr

So speed of first train is 12.5*7 = 87.5 km/hr

42. The distance from town A to town B is five miles. C is six miles from B. Which of the

following could be the maximum distance from A to C?

A) 11 B) 8

C) 2 D) 4

Answer &ExplanationAnswer: A) 11

Explanation:


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Do not assume that AB and C are on a straight line. Make a diagram with A and B marked 5

miles apart. Draw a circle centered on B, with radius 6. C could be anywhere on this circle.

The minimum distance will be 1, and maximum 11

43. A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover

the same distance downstream, if the speed of current is one-fourth the speed of the boat in

still water:

A) 1.8h B) 3h

C) 4h D) 5h

Answer &ExplanationAnswer: B) 3h

Explanation:

Upstream speed = B-S

Downstream speed = B+s

B-S = 15/5 = 3 km/h

Again B= 4S

Therefore B-S = 3= 3S

=> S = 1 and B= 4 km/h

Therefore B+S = 5km/h

Therefore, Time during downstream = 15/5 = 3h

44. A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

A) 3.6 B) 7.2

C) 8.4 D) 10

Answer &ExplanationAnswer: B) 7.2

45. Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively.

What time will they take to be 8.5km apart, if they walk in the same direction?

A) 15 hours B) 16 hours

C) 17 hours D) 18 hours

Answer &ExplanationAnswer: C) 17 hours


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Explanation:

In this type of questions we need to get the relative speed between them,

The relative speed of the boys = 5.5kmph – 5kmph

= 0.5 kmph

Distance between them is 8.5 km

Time = Distance/Speed

Time= 8.5km / 0.5 kmph = 17 hrs

46. The distance of the college and home of Rajeev is 80km. One day he was late by 1 hour

than the normal time to leave for the college, so he increased his speed by 4km/h and thus he

reached to college at the normal time. What is the changed (or increased) speed of Rajeev?

A) 28 km/h B) 30 km/h

C) 40 km/h D) 20 km/h

Answer &ExplanationAnswer: D) 20 km/h

Explanation:

Let the normal speed be x km/h, then

x = 16 km/h

(x + 4) = 20 km/h

Therefore increased speed = 20 km/h

47. A train with 120 wagons crosses Arun who is going in the same direction, in 36 seconds.

It travels for half an hour from the time it starts overtaking the Arun ( he is riding on the

horse) before it starts overtaking the Sriram( who is also riding on his horse) coming from the

opposite direction in 24 seconds. In how much time (in seconds) after the train has crossed

the Sriram do the Arun meets to Sriram?

A) 3560 sec B) 3600 sec

C) 3576 sec D) can't be determined


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Answer &ExplanationAnswer: C) 3576 sec

Explanation:

Let the length of the train be L metres and speeds of the train Arun and Sriram be R, A and S

respectively, then

---------- (i)

and ---------(ii)

From eq.(i) and (ii)

3(R - A ) = 2 (R + K)

R = 3A + 2K

In 30 minutes (i.e 1800 seconds), the train covers 1800R (distance) but the Arun also covers

1800 A (distance) in the same time. Therefore distance between Arun and Sriram, when the

train has just crossed Sriram

= 1800 ( R - A) - 24 ( A + K)

Time required =

= (3600 - 24) = 3576 s

48. A train overtakes two girls who are walking in the opposite direction in which the train

is going at the rate of 3 km/h and 6km/h and passes them completely in 36 seconds and 30

seconds respectively. The length of the train is:

A) 120m B) 150m

C) 125m D) None of these

Answer &ExplanationAnswer: B) 150m

Explanation:

Let the length of the train e x meter, and let the speed of train be y km/h, then

and

From eq (1) and (2), we get

y = 12 km/h

x= 150 m


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49. If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of

60km. what is the usual speed of Deepesh?

A) 100 B) 120

C) 150 D) None of these

Answer &ExplanationAnswer: A) 100

Explanation:

Let the original speed be x km/h, then

original speed = 100km/h

50. Shahrukh starts from Barabanki to Fatehpur , 1 hour after Ajay starts. Shahrukh meets

Kajol 1.5 hours after Shahrukh starts. If the speed of Shahrukh is at least 20km/h faster than

the speed of Kajol.

What is the minimum speed of Shahrukh to overtake Ajay, before he meets Kajol?

A) 30 B) 40

C) 60 D) None of these

Answer &ExplanationAnswer: D) None of these

Explanation:

Let t be the time after Kajol starts, when she meets Ajay, then

This should be less than 2.5 or (x+y)>120

Since y=

This (y>72) is greater than 67.5 km/h and hence Shahrukh will always overtake Ajay before

he meets Kajol.

51. A train covers a distance in 50 minutes, if it runs at a speed of 48kmph on an average.

Find the speed at which the train must run to reduce the time of journey to 40 minutes.

A) 50 km/hr B) 60 km/hr

C) 65 km/hr D) 70 km/hr


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Answer &ExplanationAnswer: B) 60 km/hr

Explanation:

We are having time and speed given, so first we will calculate the distance. Then we can get

new speed for given time and distance.

Lets solve it.

Time = 50/60 hr = 5/6 hr

Speed = 48 mph

Distance = S*T = 48 * 5/6 = 40 km

New time will be 40 minutes so,

Time = 40/60 hr = 2/3 hr

Now we know,

Speed = Distance/Time

New speed = 40*3/2 kmph = 60kmph

52. A person goes to his office at 1/3rd of the speed at which he returns from his office. If the

average speed during the whole trip is 12 m /h .what is the speed of the person while he was

going to his office?

A) 10 B) 6

C) 8 D) can't be determined

Answer &ExplanationAnswer: C) 8

Explanation:

u = k , v= 3k

53. Akash leaves mumbai at 6 am and reaches Bangalore at 10 am . Prakash leaves

Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?

A) 10 am B) 8:32 am

C) 8:56 am D) 9:20 am

Answer &ExplanationAnswer: C) 8:56 am

Explanation:


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Time taken by Akash = 4 h

Time taken by Prakash = 3.5 h

For your convenience take the product of times taken by both as a distance.

Then the distance = 14km

Since, Akash covers half of the distance in 2 hours(i.e at 8 am)

Now, the rest half (i.e 7 km) will be coverd by both prakash and akash

Time taken by them = 7/7.5 = 56 min

Thus , they will cross each other at 8 : 56am.

54. A motor boat takes 12 hours to go downstream and it takes 24 hours to return the same

distance. what is the time taken by boat in still water?

A) 15 h B) 16 h

C) 8 h D) 20 h

Answer &ExplanationAnswer: B) 16 h

Explanation:

If t1 and t2 are the upstream and down stream times. Then time taken in still water is given

by

55. Arjun and Bhishma are running on a circular track of length 600m. Speed of Arjun is 30

m/s and that of Bhishma is 20 m/s .They start fro the same point at the same time in the same

direction. When will they meet again for the first time?

Answer

Sol :

Actually Arjun has to make a lead of 600 m, because when Arjun will be 600m ahead of

Bhishma, they will be together again as a person when completes the total length it starts

retracing he same path and thus Arjun and Bhishma can be together again.

Since , they make a difference of 10 m in 1 second. so, he will create 600m difference in 60

second.


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56. Den Bosch and Eastbourne are two famous cities 300 km apart. Maradona starts from

Den Bosch at 8:24 am . An hour later pele starts from Den Bosch. After travelling for 1 hour ,

Pele reaches Nottingham that Maradona had passed 40 minutes earlier. Nottingham falls on

the way from Den Bosch to Eastbourne. If pele and Maradona just reaches Eastbourne at the

same time, what are thespeeds of the Maradona and Pele Respectively?

A) 100 km/h , 125 km/h B) 60 km/h , 80 km/h

C) 60 km/h , 75 km/h D) 75 km/h , 100 km/h

Answer &ExplanationAnswer: D) 75 km/h , 100 km/h

Explanation:

Let Pele x km in 1 hour. soMaradona takes (2h-40min)=1 h 20 min to cover x km. Let speed

of Maradona and Pele be M and P respectively than

x = and x= P x 1

Again

k= 25

M= 3k = 75 km/h

and P= 4k = 100 km/h

( Through options it is very easy to solve)

57. A man goes down stream with a boat to some destination and returns upstream to his

original place in 5 hours. If the speed of the boat in still water and the strean are 10km/hr and

14km/hr respectively, the distance of the destination from the string place is

A) 16 km B) 18 km

C) 21 km D) 25 km

Answer &ExplanationAnswer: C) 21 km

Explanation:

Let the distance covered be D km.

km


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58. A and B runs around a circular track. A beats B by one round or 10 minutes. In this race,

they had completed 4 rounds. If the race was only of one round, find the A's time over the

course:

A) 8 min B) 7.5 min

C) 12.5 min D) 12 min

Answer &ExplanationAnswer: B) 7.5 min

Explanation:

B runs around the track in 10 min.

i.e , Speed of B = 10 min per round

A beats B by 1 round

Time taken by A to complete 4 rounds

= Time taken by B to complete 3 rounds

= 30 min

A's speed = 30/4 min per round

= 7.5 min per round

Hence, if the race is only of one round A's time over the course = 7 min 30 sec

59. A Person X started at 3 hours earlier at 40km/h from a place P, then another person Y

followed him at 60km/h. Started his journey at 3 O'clock, afternoon. What is the diference in

time when X was30 km ahead of Y and when Y was 30 km ahead of X?

A) 2h B) 3h

C) 3.5h D) 4.25h

Answer &ExplanationAnswer: B) 3h

Explanation:

Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h

Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h

Thus, required difference in time = 3h

60. Two trains starting at the same time from two stations 200 km apart and going in opposite

directions cross each other at a distance of 110 km from one of the stations. What is the ratio

of their speeds?

A) 9 : 20 B) 11 : 9

C) 11 : 20 D) None of these

Answer &ExplanationAnswer: B) 11 : 9


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Explanation:

In the same time, they cover 110 km and 90 km respectively.

Ratio of their speeds = 110 : 90 = 11 : 9

61.In a race of 800m Kaushik gives Piyush a start of 200m and then loses the race by 20

seconds. What is the speed of Piyush and Kaushikrespectively ?If the ratio of respective

speeds be 3:2.

Answer

Let the speed of Kaushik be and speed of Piyush be and let the time taken by

Piyushbe t second then,

t = 20 s

Speed of Piyush =

and Speed of Kaushik =

62. In 12 hours how many times the two hands of clock will be just opposite to each other i.e,

they make a straight line having the difference of 180 degrees between them?

Answer

Sol : = 30 points

For the first time minute- hand and hour-hand will be seperated in

and for every next time they will take minutes more to occur as opposite to each other.


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( since in 60/55 hours they complete one round of clock's daili.e , 60npoints undergoing the

relative motion, we have total 12 hours)

Thus ,

only integral value is admissible.

Thus, total 10+1 =11 times both hands of a clock will be oppositeb to each other.

63. Uday travels half of his journey by train at the speed of 120 km/h and rest half by car at

80 Km/h.What is the average speed?

Answer

Let the total distance be 2D km, then

Total time = Time taken by train + Time taken by car =

Therefore, Average speed=

=


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64. A train of length 250 m crosses a bridge of length 150m in 20 seconds. What is the speed

of train?

Answer

Sol : (length of train+ length of bridge) = speed of train x Time

(250+150) = 20 x Speed

Speed = 400/20= 20 m/s =72 km/h

65. A man can row 9 km/h in still water. It takes him twice as long as to row down. Find the

rate of stream of the river ?

Answer

=

= where

B ---> speed of boat in still water

R---->speed of current

( Bycomponendo and dividendo)

time speed and idistance

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