TIME & DISTANCE

REASONING AND QUANTITATIVE APTITUDE Time & Distance 

SITAMS 

TIME 

& 

DISTANCE 

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MODULE OBJECTIVE: 

Decision making for planning, policy, and management relies increasingly on 

quantitative reasoning, which entails the collection, analysis and interpretation of 

quantitative data. This course is designed to introduce principles and techniques to solve 

time and distance related problems. 

Develop Logical Reasoning in a Problem-Solving Framework. One goal is to 

develop a disciplined logical analysis of “word” problems. Such reasoning is the 

foundation for building simple mathematical models of problems – models implicit in 

counting time and distance. A good way to learn this logical thinking is by working many 

exercises. Students will use this reasoning often (consciously or unconsciously) in 

computer science, operations research, and probability and statistics. However, a logical 

mind will serve a person well in ANY field. 

At the end of these course students: 

• To be understood the types of formulae are used to measure time and Distance. 

• To be able to calculate time and distance while an object that moves at a constant 

rate is said to be in uniform motion, Uniform motion problems may involve 

objects going the same direction, opposite directions, or round trips. 

• To be solving many problems related to time and distance and which can be useful 

to students to face interviews. 

C. PREREQUISITIES (Important Formulas): 

SITAMS 

i) Speed = Distance/Time 

ii) Time = Distance/speed 

iii) Distance = speed*time 

iv) 1km/hr = 5/18 m/s 

v) 1 m/s = 18/5 Km/hr 

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 

viii) An object that moves at a constant rate is said to be in uniform motion. The 

formula d = rt gives the relationship between distance d, rate r, and time t. 

Uniform motion problems may involve objects going the same direction, 

opposite directions, or round trips. 

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D. Solved Examples: 

1.) Walking at the rate of 4kmph a man cover certain distance in 2hr 45 min. Running at a 

speed of 16.5 kmph the man will cover the same distance in. 

A. 12 min B. 25 min C. 40min D. 60 min 

Answer: Option C 

Explanation: Distance = Speed * time 

4*11/4 = 11km 

New Speed = 16.5 kmph 

Therefore time = D/S = 11/16.5 = 40min 

2.) 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. 

A. 45 min B. 60 min C. 75 min D. None of these 

Answer: Option B 

Explanation: 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 

3.) 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. 17 hrs B. 25 hrs C. 31 hrs D. 45 hrs 

Answer: Option A 

Explanation: 

SITAMS 

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 

4.) 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. 4 B. 6 C. 8 D. None of these 

Answer: Option D 

Explanation: 

Due to stoppages, it covers 9 km less. 

Time taken to cover 9 km = (9/54 x 60) min = 10 min. 

3


5.) 2 trains starting at the same time from 2 stations 200km apart and going in opposite 

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

ratio of their speeds? 

A. 7:3 B. 11:9 C. 18:4 D. None of these 


Explanation: 

SITAMS 

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

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

6.) In covering a distance of 30 km, Sachin takes 2 hours more than Rohit. If Sachin 

doubles his speed, then he would take 1 hour less than Rohit. Sachin speed is: 

A. 5 kmph B. 16 kmph C. 21 kmph D. None of these 


Explanation: 

Let Sachin’s speed be X km/hr. 

Then, 30/x - 30/2x = 3 

6x = 30 

x = 5 km/hr. 

7.) A train 140m long running at 60kmph. In how much time will it pass a platform 260m 

long? 

A. 5 kmph B. 16 kmph C. 21 kmph D. None of these 


Explanation: 

Distance travelled = 140 + 260m = 400m, 

Speed = 60 * 5/8 = 50/3m 

Time = 400 * 3/50 = 24 Seconds 

8.) The ratio between the speeds of two trains is 7: 8. If the second train runs 440 kms in 4 

hours, then the speed of the first train is: 

A. 47.4 km/hr B. 57.19 km/hr C. 68.13 km/hr D. None of these 


Explanation: 

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

Then, 8x = (440/4) = 110 

x = (110/8) = 13.75 

Speed of first train = (7 x 13.75) km/hr = 96.25 km/hr. 

4


9.) Sachin 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? 

A. 5km B. 6km C. 7km D. 8km 


Explanation: 

SITAMS 

Distance = 2/3S 

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

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

84=14/3S * 3 

S= 6km 

10.) A person walks at 5kmph for 6hr and at 4kmph for 12hr.The average speed is. 

A. 4 1/3 B. 7 2/3 C. 9 ½ km D. 8km 


Explanation: 

Avg speed = total distance/total time 

= 5*6 + 4*12 / 18 

=4 1/3 mph 

11)A person covers a certain distance at 7kmph .How many meters does he cover in 

2 minutes. 

A) 14 kmph B) 7 kmph C) 2400m D) 1200m 


Explanation: 

Speed=72kmph=72*5/18 = 20m/s 

Distance covered in 2min =20*2*60 = 2400m 

12)If a man runs at 3m/s. How many km does he run in 1hr 40min 

A) 18 km B) 7 km C) 12 km D) 17 km 


Explanation: 

Speed of the man = 3*18/5 kmph = 54/5kmph 

Distance covered in 5/3 hrs=54/5*5/3 = 18km 

13)A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The 


A) 18 kmph B) 60 km ph C) 30 kmph D) 50 kmph 


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Explanation: 

SITAMS 

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 

14)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? 

A) 18 km B) 6 km C) 12 km D) 17 km 


Explanation: 

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 

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

the usual time is. 

A) 4 B) 7 ½ C) 7 D) 5 


Explanation: 

Usual speed = S 

Usual time = T 

Distance = D 

New Speed is ¾ S 

New time is 4/3 T 

4/3 T – T = 5/2 

T=15/2 = 7 ½ 

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E. EXERCISE PROBLEMS: 

1)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:: 

SITAMS 

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 

2)Excluding stoppages, 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 

3)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. 

Solution:: 

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 

4)2 trains starting at the same time from 2 stations 200km apart and going in opposite 

direction cross each other at a 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 

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5)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:: 

SITAMS 

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= 600 

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

6)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 

7) In covering distance, the speed of A & B are in the ratio of 3:4.A takes 30min more 

than B to reach the destination. The time taken by A to reach the destination 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 

8)A person covers a certain distance at 7kmph .How many meters does he cover in 2 

minutes. 

Solution:: 

speed=72kmph=72*5/18 = 20m/s 

distance covered in 2min =20*2*60 = 2400m 

8


9)If a man runs at 3m/s. How many km does he run in 1hr 40 min 

Solution:: 

SITAMS 

speed of the man = 3*18/5 kmph = 54/5kmph 

Distance covered in 5/3 hrs=54/5*5/3 = 18km 

10)Walking at the rate of 4knph a man covers certain distance in 2hr 45 min. Running at a 

speed of 16.5 kmph the man will cover the same distance in. 

Solution:: 

Distance=Speed* time 4*11/4=11km 

New speed =16.5kmph 

therefore Time=D/S=11/16.5 = 40min 

11)A train covers a distance in 50 min ,if it runs at a speed of 48kmph on an average.The 


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 

12)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 

13)Excluding stoppages,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 

14)A motorist covers a distance of 39km in 45min by moving at a speed of xkmph for the 

first 15min.then moving at double the speed for the next 20 min and then again moving at 

his original speed for the rest of the journey .then x=? 

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Solution:: 

SITAMS 

Total distance = 39 km 

Total time = 45 min 

D = S*T 

x * 15/60 + 2x * 20/60 + x * 10/60 = 39 km 

x = 36 kmph 

15)A & B are two towns. Mr.Fara covers the distance from A to B on cycle at 17kmph 

and returns to A by a tonga running at a uniform speed of 8kmph.his average speed 

during the whole journey is. 

Solution:: 

When same distance is covered with different speeds, then the average speed = 2xy / x+y 

=10.88kmph 

16)A car covers 4 successive 3km stretches at speed of 10kmph,20kmph,30kmph & 

60kmph resp. Its average speed is. 

Solution:: 

Average speed = total distance / total time 

total distance = 4 * 3 = 12 km 

total time = 3/10 + 3/20 + 3/30 + 3/60 

= 36/60 hr 

speed =12/36 * 60 = 20 kmph 

17)A person walks at 5kmph for 6hr and at 4kmph for 12hr. The average speed is. 

Solution:: 

avg speed = total distance/total time 

= 5*6 + 4*12 / 18 

=4 1/3 mph 

18)A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey 

in 3/5th time.wht should be its speed to cover the remaining distance in the time left. 

Solution:: 

Time left = 10 – 3/5*10 

= 4 hr 

speed =40 km /4 hr 

=10 kmph 

19)The ratio between the speeds of the A& B is 2:3 an therefore A takes 10 min more 

than the time taken by B to reach the destination. If A had walked at double the speed ,he 

would have covered the distance in ? 

Solution:: 

Ratio of speed = 2:3 

Ratio of time = 3:2 

A takes 10 min more 

10


SITAMS 

3x-2x = 10 min 

A time=30 min 

�A covers the distance in 30 min , if its speed is x 

-> He will cover the same distance in 15 min, if its speed 

doubles (i.e 2x) 

20)A is twice as fast as B and B is thrice as fast as C is. The journey covered by B in? 

Solution:: 

speed& ratio 

a : b = 2: 1 

b : c = 3:1 

Time& ratio 

b : c = 1:3 

b : c = 18:54 

(if c covers in 54 min i..e twice to 18 min ) 

21)A man performed 3/5 of the total journey by ratio 17/20 by bus and the remaining 

65km on foot.wht is his total journey. 

Solution:: 

Let total distance is x 

x-(3/5x + 17/20 x) =6.5 

x- 19x/20 = 6.5 

x=20 * 6.5 

=130 km 

22)A train M leaves Meerat at 5 am and reaches Delhi at 9am . Another train N leaves 

Delhi at 7am and reaches Meerut at 1030am At what time do the 2 trains cross one 

Another 

Solution:: 

Let the distance between Meerut & Delhi be x 

they meet after y hr after 7am 

M covers x in 4hr 

N covers x in 3 ½ i.e 7/2 hr 

speed of M =x/4 

speed of N = 2x/7 

Distance covered by M in y+2 hr + Distance covered by N in 

y hr is x 

x/4 (y+2) +2x/7(y)=x 

y=14/15hr or 56 min 

23)A man takes 5hr 45min in walking to certain place and riding back. He would have 

gained 2hrs by riding both ways. The time he would take to walk both ways is? 

Solution:: 

Let x be the speed of walked 

Let y be the speed of ride 

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SITAMS 

Let D be the distance 

Then D/x + D/y = 23/4 hr -------------------------1 

D/y + D/y = 23/4 – 2 hr 

D/y = 15/8 -------------------------------------------2 

substitute 2 in 1 

D/x + 15/8 = 23/4 

D/x = 23/4 -15/8 =46-15/8 =31/8 

Time taken for walk one way is 31/8 hr 

time taken to walk to and fro is 2*31/8 = 31/4 hr 

=7 hr 45 min 

24. EngineeringA train leaves a train station at 1 p.m. It travels at an average rate of 60 

mi/h. A high-speed train leaves the same station an hour later. It travels at an average rate 

of 96 mi/h. The second train follows the same route as the first train on a track parallel to 

the first. In how many hours will the second train catch up with the first train? 

Solution: 

25. Noya drives into the city to buy a software program at a computer store. Because of 

traffic conditions, she averages only 15 mi/h. On her drive home she averages 35 mi/h. If 

the total travel time is 2 hours, how long does it take her to drive to the computer store? 

12


26. Jane and Peter leave their home traveling in opposite directions on a straight road. 

Peter drives 15 mi/h faster than Jane. After 3 hours, they are 225 miles apart. Find Peter's 

rate and Jane's rate. 

27.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 


SITAMS 

13


Explanation: 

Speed=(600/5 * 60) m/sec 

SITAMS 

= 2 m/sec. 

Converting m/sec to km/hr (see important formulas section) 

=(2*18/5) km/hr 

= 7.2 km/hr. 

28. 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 


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 * 3/5) km/hr= 720 km/hr. 

29. 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 


Explanation: 

Let the actual distance travelled be x km. 

Then x/10=(x+20)/14 

14x = 10x + 200 

4x = 200 

x = 50 km. 

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30. 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: 



SITAMS 


Explanation: 

Let speed of the car be x kmph. 

Then, speed of the train=(150/100)*x=(3/2)*x kmph 

(75/x)-(75/(3/2x))=125/(10*60) 

(75/x)-(50/x)=5/24 

x = 25 x24 = 120 kmph. 

5 

31. 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 


Explanation: 

Due to stoppages, it covers 9 km less. 

Time taken to cover 9 km = 9 x 60 min = 10 min. 

54 

32. 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 


Explanation: 

Let the duration of the flight be x hours. 

Then, 600- 600 = 200 

15


SITAMS 

x x + (1/2) 

600 - 1200 = 200 

x 2x + 1 

x(2x + 1) = 3 

2x 2 + x - 3 = 0 

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

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

33. 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 


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 

34. 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. 70 km/hr B.75 km/hr 

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


Explanation: 

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

Then, 8x = 400 = 100 

4 

x = 100 = 12.5 

8 

16


SITAMS 

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

35. 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 


Explanation: 

Total time taken = 160 + 160 

hrs. =9 64 80 

hrs. 

2 

Average speed = 320 x 2 

9 

= 71.11 km/hr. 

km/hr 

36. 

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 

B.25 km/hr 

7 

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


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 

37. 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: 


C. 6.25 kmph D.7.5 kmph 


Explanation: 

17


SITAMS 

Let Abhay's speed be x km/hr. 

Then, 30 - 30 = 3 

x 2x 

6x = 30 

x = 5 km/hr. 

38. 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.? 




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 

10 

= 6 hrs. 

hrs 

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

Required speed = 60 

5 

= 12 kmph. 

kmph. 

39. 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 


Explanation: 

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

18


Then, 120 + 480 = 8 1 + 4 = 1 x y 

....(i) 

x y 15 

And, 200 + 400 = 25 

x y 3 

1 2 1 

+ = ....(ii) 

x y 24 

SITAMS 

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

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

40. 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 


Explanation: 

Let the distance travelled on foot be x km. 

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. 

41. 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 

D.40 

2 


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 

19


SITAMS 

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

Each of the questions given below consists of a statement and / or a question and two 

statements numbered I and II given below it. You have to decide whether the data 

provided in the statement(s) is / are sufficient to answer the given question. Read the both 

statements and 

• Give answer (A) if the data in Statement I alone are sufficient to answer the 

question, while the data in Statement II alone are not sufficient to answer the 

question. 

• Give answer (B) if the data in Statement II alone are sufficient to answer the 

question, while the data in Statement I alone are not sufficient to answer the 

question. 

• Give answer (C) if the data either in Statement I or in Statement II alone are 

sufficient to answer the question. 

• Give answer (D) if the data even in both Statements I and II together are not 

sufficient to answer the question. 

• Give answer(E) if the data in both Statements I and II together are necessary to 

answer the question. 

42. Two towns are connected by railway. Can you find the distance between them? 

I. The speed of the mail train is 12 km/hr more than that of an express train. 

II. A mail train takes 40 minutes less than an express train to cover the distance. 

A. I alone sufficient while II alone not sufficient to answer 

B. II alone sufficient while I alone not sufficient to answer 

C. Either I or II alone sufficient to answer 

D. Both I and II are not sufficient to answer 

E. Both I and II are necessary to answer 


Explanation: 

Let the distance between the two stations be x km. 

I. Then, speed of the mail train = (y + 12) km/hr. 

II. x x 40 

- = . 

y (y + 12) 60 

Thus, even I and II together do not give x. 

Correct answer is (D). 

20


43. The towns A, B and C are on a straight line. Town C is between A and B. The 

distance from A to B is 100 km. How far is A from C? 

I. The distance from A to B is 25% more than the distance from C to B. 

II. The distance from A to C is of the distance C to B. 






SITAMS 


Explanation: 

.__________.______________________________________. 

A x C (100 - x) B 

Let AC = x km. Then, CB = (100 -x) km. 

I. AB = 125% of CB 

100 = 125 x (100 - x) 

100 

100 - x = 100 x 100 = 80 

125 

x = 20 km. 

AC = 20 km. 

Thus, I alone gives the answer. 

II. AC = 1 CB 

4 

x = 1 (100 - x) 

4 

x = 100 

x = 20. 

AC = 20 km. 

Thus, II alone gives the answer. 

Correct answer is (C). 

21


44. Two cars pass each other in opposite direction. How long would they take to be 500 

km apart? 

I. The sum of their speeds is 135 km/hr. 

II. The difference of their speed is 25 km/hr. 






SITAMS 


Explanation: 

I gives, relative speed = 135 km/hr. 

Time taken = 500 hrs. 

135 

II does not give the relative speed. 

I alone gives the answer and II is irrelevant. 

Correct answer is (A). 

45. How much time did X take to reach the destination? 

I. The ratio between the speed of X and Y is 3 : 4. 

II. Y takes 36 minutes to reach the same destination. 






Answer: Option E 

Explanation: 

Since ratio of speed of X : Y is 3 : 4, then ratio of time will be 4 : 3. 

I. If Y takes 3 min, then X takes 4 min. 

II. If Y takes 36 min, then X takes 4 x 36 min = 48 min. 

3 

Thus, I and II together give the answer. 

Correct answer is (E). 

22


F. QUESTION BANK MOCK TEST 

1. Express a speed of 54 km/hr in meters/second. 

a)15 m/sec b)20 m/sec c)25 m/sec d)30 m/sec 

2.A car can cover 350 km in 4 hours. If the speed is decreased by 12 1/2 kmph, how much 

time does the car take to cover a distance of 450 km? 

a)4 hrs b)5 hrs c)2 hrs d)6 hrs 

3.A person covers a certain distance at a certain speed. If he increases his speed by 25 % 

then he takes 12 minutes less to cover the same distance. Find the time taken by him 

initially to cover the distance at the original speed 

a)3 hrs b)2 hrs c)1 hr d)7 hrs 

4.A car covers a certain distance going at a speed of 60 kmph and returns to the starting 

point at a speed of 40 kmph.Find the average speed for the whole journey. 

a)48 kmph b)42 kmph c)34 kmph d)40 kmph 

5.What is the time taken by a train running at 54 km/hr to cross a man standing on a 

platform, the length of the train being 180 m? 

a)6 seconds b)12 seconds c)16 seconds d)18 seconds 

6.How long will a train 100 m long and travelling at a speed of 45 kmph,take to corss a 

platform of length 150 m? 

a)20 sec b)29 sec c)27 sec d)cannot be determined 

7.Find the length of the bridge,which a train 120 m long travelling at 54 kmph can cross 

in 30 seconds. 

a)340 m b)350 m c)330 m d)390 m 

SITAMS 

23


8.A worker reaches his work place 15 minutes late by walking at 4kmph from his house. 

The next day he increases his speed by 2kmph and reaches in time. Find the distance from 

his house to his work place 

a)2 km b)6 km c)8 km d)3 km 

9.A person leaves his house and travelling at 4 kmph reaches his office 10 minutes late. 

Had he travelled at 7kmph he would have been 20 mins early. Find the distance from the 

house to the office? 

a)14/3 b)2 c)14/9 d)14/6 

10.Find the time taken by a train 150 m long running at a speed of 63 kmph to cross 

another train of length 100 m long running at a speed of 45 kmph in the same direction 


11.A train crosses two persons, cycling in the same direction as the train in 12 and 18 

seconds respectively. If the speeds of the two cyclists are 9 and 18 kmph respectively. 

Find the length and speed of the train. 

a)80 m b89 m c)98 m d)90 m 

12.Two trains running at 45 and 54 kmph cross each other in 12 seconds when they run in 

opposite directions. When they run in the same direction, a person in the faster train 

observes that he crossed the other train in 32 seconds. Find the lengths of the two trains 

a)250 b)450 c)260 d)234 

13.Two trains of length 150 m and 250m run on parallel lines. When they run in the same 

direction it will take 20 seconds to cross each other and when they run in opposite 

direction it will take 5 seconds. Find the speeds of the two trains. 

a)180 and 108 b)272 and 211 c)123 and 828 d)none of these 

SITAMS 

24


14.The average speed for an entire journey is 60 kmph without considering the stoppages. 

When the stoppages are considered the average speed becomes 48 kmph. How many 

minutes per hour on an average were the stoppages? 

a)10 mins b)12 mins c)16 mins d)none of these 

15.I had to catch a bus which was 225 m ahead of me. The bus also started at the same 

time. If the speed of the bus was 2.5 m/sec and my speed was 36 kmph, in how much time 

can i catch the bus? 


16.The distance from my house to my friends house is 12 km. I walked at a speed of 4 

kmph and after every kilometre took rest for 10 mins.How much time did it take for me to 

reach my friends house? 

a)3 hrs b)4 hrs and 50 mins c)5 hrs d)none of these 

17.A train covered a distance of 250 km,partly at an average speed of 40 kmph and partly 

at 60 kmph. Find the distance covered at 40 kmph if it took 5 hrs for the train to cover the 

distance. 

a)150 km b)120 km c)100km d)cannot be determined 

18.A bus covered a distance of 160 km in 4 hrs covering a part of it at 30 kmph and the 

remaining at 70 kmph.For how much time did the us travel at 70 kmph? 

a)0.5 hr b)1 hr c)1 1/2 hs d)2 hrs 

19.A car takes 2 hours more to cover a distance of 480 km when its speed is reduced by 8 

kmph. Find its usual speed 


SITAMS 

25


20.A person covered the first 40 km of his journey at 50 kmph,the next 70 km at 35 kmph 

and the remaining distance in 12 mins. If the average speed of the entire journey is 52 

kmph. Find the distance covered in the last stench of the journey. 

a)22 km b)34 km c)40 km d)46 km 

21.A train takes 10 seconds to cross a man standing on a platform and 44 seconds to cross 

the platform. What is the length of the platform. What is the length of the platform if the 

speed of the train is 72 kmph? 

a)440 m b)570 m c)680 m d)none of these 

22.A train travelling at 36 kmph takes 48 seconds to cross a bridge. It then crosses a man 

cycling at the rate of 9 kmph in the same direction in 20 seconds. Find the length of the 

bridge 

a)150 m b)220 m c)280 m d)330 m 

23.A train crosses two bridges 370 m and 480 m long in 51 and 62 seconds respectively. 

Find the speed of the train. 


24.A man started 15 minutes late and by travelling at a speed which is 5/4rth of his usual 

speed reached his office 20 mins early. What is the usual time of the journey? 

a)85mins b)100 mins c)135 mins d)175 mins 

25.A parachutist,before he opens his parachute,falls for a time t1,and covers a distance of 

5t1^2 and after he opens his parachute he falls for a time t2 and covers a distance Vt2.V is 

the velocity attained just before the parachute is opened and is given by 5t1.After what 

time did he open the parachute,if the total distance covered by the parachutist is 1500m 

and the total time is 30 seconds? 


SITAMS 

26


26.Akash,Anurag and Rishab are running around a circular track of length 900 m with 

respective speeds of 15 m , 20 m and 30 m/sec.Akash and Anurag are running in the same 

direction while Rishab is running in the opposite direction.After how much time will all 

the three of them meet for the first time? 


27.A police patrol party travelling at 60 kmph crosses an escaping thief travelling in the 

opposite direction at 48 kmph.The police party has to travel for a further 5 minutes before 

it can find a gap in the median where it can take a U turn and start chasing the thief.After 

how much time after the police party crosses the thief does it catch him? 

a)25 mins b)50 mins c)15 mins d)32 mins 

28.In a 1000 m race A reaches the goal 5 seconds earlier and beats B by 50 m.What is A's 

speed? 

a)10 m/s b)10 10/19 m/s c)9 9/19 m/s d)11 9/19 m/s 

29.Two points A and B are diametrically opposite points on a circular road of 

circumference 12 km. A cyclist started from A and made three rounds.He made the first 

round with a speed of 12 kmph and decreased his speed by 3 kmph for every round.What 

is the interval between the first time he passes through B and the third time he passes 

through B? 

a)200 mins b)100 mins c)85 mins d)170 mins 

30.Two men left simultaneously two places A and B.One of them left A for B while the 

other left B for A.Both travel each at his own uniform velocity.The first person on 

reaching B returns to A and then again travels bach to B and so on.What will be the 

distance covered by the first person when they meet for the third time given the ratio of 

the speed of the first person to that of the second person is 3:2 the distance between A and 

B is 500 m? 

a)1000 m b)1500 m c)2500 m d)1200 m 

SITAMS 

27


31.A person takes 6 hours to go by car to a certain place and return by bus.He gains 2 hrs 

if he goes both ways by car.How long would he have taken if he had gone by bus both 

ways? 

a)4 hrs b)6 hrs c)8 hrs d)2 hrs 

32.car A and car B are travelling on two perpendicular roads towards city C with equal 

speeds. car A starts from a distance of 100 km ar 11 a.m while car B starts from a 

distance of 70 km at 12 noon. At 2p.m the two cars are 50 km apart. What is the speed 

with which they are travelling? 


33.Two trains of length 200 m and 100 m simultaneously wnter a tunnel of length 300m 

from opposite ends at the same time on parallel tracks.The respective speeds of the two 

trains are 36 kmph and 18 kmph.After how much time from the instant the two trains 

entered the tunnel will the tunnel be free of traffic again? 


34.Rajat had covered one third of the total distance of his trip when his scooter failed .He 

then parked it and covered the remaining distance on foot, spending 20 times as long 

walking as riding. How many times was his riding speed more than his walking speed? 

a)20 b)19 c)10 d)9 

35.Ashish and Bali run towards each other from P and Q respectively with respective 

speeds of 36 kmph and 45 kmph.After meeting each other if Ashish reaches Q in 5 

hours,in how many hours will Bali reach P? 

a)3 b)3 1/5 c)4 d)8 

SITAMS 

28


36.A train of length 180 m travelling at 72 kmph overtook a motorcyclist travelling at 36 

kmph at 4 p.m. At 5 p.m it overtook another cyclist travelling in the opposite direction at 

a speed of 18 kmph.When will the cyclist meet the motorcyclist? 

a)1 hr 20 mins b)1 hr 30 min c)1 hr 45 min d)none of the above 

37.Two men left simultaneously two places A and B. one of them left A for B and the 

other B for A. Both travelled each with his own uniform velocity. Having arrived at their 

destination, they turned back without stopping and turned back to their starting points. 

First time, they met on their own journey 18 km from B; the second time on their return 

journey 9 km from A. Find the distance AB. 

a)30 km b)45 km c)60 km d)cannot be determined 

38.A car travels a total distance of 150 km. After travelling a part of the distance without 

any trouble ,the car develops an engine problem and proceeds at 2/3rd of its former speed 

and arrives at the destination 48 mins late. Had the problem developed 24 km further on, 

the car would have arrived 12 min sooner. Find the original distance it travelled without 

any problem and the speed over that part of the journey. 

a)100km,60 kmph b)48km,36kmph c)72km,50kmph d)54km,60 kmph 

39. Two cyclists simultaneously start from A to B and B to A respectively. They cross 

each other after a time t hours. The first person reaches B in another t1 hours while the 

second person reaches A in another t2 hours. Then 

a)t=t1+t2/2 b)t=2t1t2/t1+t2 c)t=sqrt(t1t2) d)t=t2-t1/2 

40.Ramu starts from P towards Q at a speed of 30 kmph and after every 12 min increase 

his speed by 5 kmph. If the distance between P and Q is 52 km, then how much time does 

he take to cover the distance? 

a)60 min b)72 min c)90 min d)120 min 

SITAMS 

29

TIME & DISTANCE

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